џWPCL ћџ2BJ|xа АH аа АА X агга ХА6p&А6p&Х аеGI а HH аСр8QСааУ У Ф Ф GееЮ† а Hр аааУ Уб cмˆ4 PŽТ б Fascicle II.3 Р-Р Rec. E.508 Ф ФPAGE1У Уб cмˆ4 PŽТ б ЮееЃ† а HH аааб cмˆ4 PŽТ бPAGE8У Уб cмˆ4 PŽТ б Fascicle II.3 Р-Р Rec. E.508 Ѓеа H№ ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаа X аб cмˆ4 PŽТ бAll drawings appearing in this Recommendation have been done in Autocad. ‚У УRecommendation E.508 аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаСр(DСб cмˆ4 PŽТ бFORECASTING NEW INTERNATIONAL SERVICES аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ б1ТX ТIntroductionФ ФЦЦ а H аС СThe operation and administration of an international telecommunications network should include the consideration of subscriber demands for new services which may have different characteristics than the traditional traffic (i.e. peak busy hours, bandwidth requirements, and average call durations may be different). By addressing these new demands, Administrations can be more responsive to customer requirements for innovative telecommunications services. Based on the type of service and estimated demand for a service, network facilities and capacity may have to be augmented. An augmentation of the international network could require large capital investments and additional administrative functions and responsibilities. Therefore, it is appropriate that Administrations forecast new international services within their planning process. а H аС СThis Recommendation presents methods for forecasting new services. The definitions of some of the characteristics of these services, together with their requirements, are covered in РSР 2, followed by base data requirements in РSР 3. РSР 4 discusses research to identify the potential market. Presentation of forecasting methods are contained in РSР 5. РSР 6 concludes with forecast tests and adjustments. аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС‚У У2С  Сб cмˆ4 PŽТ бNew service definitionsЦЦ аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФ Ф2.1С  СA distinction exists between those services which are enhancements of existing services carried on the existing network and those services which are novel. С СMany of the services in this latter category will be carried on the Integrated Services Digital Network (ISDN). It is not the purpose of this section to provide an exhaustive list of services but rather to establish a framework for their classification. This framework is required because different base data and forecasting strategies may be necessary in each case. 2.2Тh  ТУ Уenhanced services offered over the existing networkФ ФЦЦ а H аС СThese are services which are offered over the existing network, and which offer an enhancement of the original use for which the network was а H аintended. Services such as the international freephone service, credit card calling and closed user groups are examples of enhancements of voice services; while facsimile, telefax and videotex are examples of nonР-Рvoice services. These services may be carried over the existing network and, therefore, data will concern usage or offered load specific to the enhancement. Arrangements can be established for the measurement of this traffic, such as the use of special network access codes for nonР-Рvoice applications or by sampling outgoing circuits for the proportion of nonР-Рvoice to voice traffic. 2.3Тh  ТУ Уnovel servicesФ ФЦЦ а H аС СNovel services are defined as totally new service offerings many of which may be carried over the ISDN. In the case of ISDN, Recommendation I.210 divides telecommunications services into two broad categories: bearer services and teleservices. Recommendation I.210 further defines supplementary services which modify or supplement a basic telecommunications service. The definition of bearer services supported by the ISDN is contained in Recommendations I.210 and I.211, while that for teleservices is found in Recommendations I.210 and I.212. Bearer services may include circuit switched services from 64 kbit/s to 2 Mbit/s and packet services. Circuit switched services above 2 Mbit/s are for further study. а H аС СTeleservices may include Group 4 facsimile, mixed mode text and facsimile, 64 kbit/s Teletex and Videotex, videophone, videoconferencing, electronic funds transfer and point of sale transaction services. These lists are not exhaustive but indicate the nature and scope of bearer services and teleservices. Examples of new services are diagrammatically presented in Table 1/E.508. ‚Ср SСб cмˆ4 PŽТ бTABLE 1/E.508 Ср FСУ УExamples of enhanced and novel servicesФ Ф б cмˆ4 PŽТ бвЦ‚H 8"Цв‡ааб cмˆ4 PŽТ б Ср RСEnhancement of Ср QСР"РNovelР"Р services а 8 ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бˆа 8 аб cмˆ4 PŽТ бвЦƒH ш`8"Цв‡Срш_Сб cмˆ4 PŽТ бexisting services Срш`СBearer services СршaСTeleservices а `8 ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бˆа `8 аб cмˆ4 PŽТ бвЦƒH ш`8"Цв‡б cмˆ4 PŽТ бTeletex Packet Group 4 facsimile а `8 аб cмˆ4 PŽТ бˆа `8 аб cмˆ4 PŽТ бвЦƒH ш`8"Цв‡б cмˆ4 PŽТ бFacsimile Mixed mode а `8 аб cмˆ4 PŽТ бˆа `8 аб cмˆ4 PŽТ бвЦƒH ш`8"Цв‡б cмˆ4 PŽТ бVideotex Videophone а `8 аб cмˆ4 PŽТ бˆа `8 аб cмˆ4 PŽТ бвЦƒH ш`8"Цв‡а `X аб cмˆ4 PŽТ бMessage handling systems Circuit switched services Videoconferencing а `8 аб cмˆ4 PŽТ бˆа `8 аб cмˆ4 PŽТ бвЦƒH ш`8"Цв‡а `а аб cмˆ4 PŽТ бInternational freephone Р-Р 64 kbit/s а `р аElectronic funds transfer а `8 аб cмˆ4 PŽТ бˆа `8 аб cмˆ4 PŽТ бвЦƒH ш`8"Цв‡б cмˆ4 PŽТ бCredit cards Р-Р 2 Mbit/s а `h аPoint of sale transactions а `8 аб cмˆ4 PŽТ бˆа `8 аб cмˆ4 PŽТ бвЦƒH ш`8"Цв‡б cмˆ4 PŽТ бClosed user groups Teletex (64 kbit/s) Videotex (64 kbit/s) а `8 аб cмˆ4 PŽТ бˆа HH ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТУ У3СјСб cмˆ4 PŽТ бBase data for forecastingЦЦ аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФ Ф3.1Тh  ТУУMeasurement of enhanced servicesЦЦ а H аФФС СMeasurements for existing services are available in terms of calls, minutes, Erlangs, etc. These procedures are covered in Recommendation E.506, РSР 2. In order to measure/identify enhanced service data from other traffic data on the same network it may be necessary to establish sampling or other procedures to aid in the estimation of this traffic, as described in РSР 4 and РSР 5. 3.2Тh  ТУУNovel servicesЦЦ а H аФФС СNovel services, as defined in РSР 2, may be carried on the ISDN. In the case of the ISDN, circuit switched bearer services and their associated teleservices will be measured in 64 kbit/s increments. Packet switched bearer services and associated teleservices will be measured by a unit of throughput, for example, kilocharacters or kilopackets per second. Other characteristics needed will reflect service quality measurements such as: noise, echo, postР-Рdialing delay, clipping, bitР-Рerror rate, holding time, setР-Рup time, errorР-Рfree seconds, etc. аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС‚У У4С  Сб cмˆ4 PŽТ бMarket researchЦЦ а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФ ФС СMarket research is conducted to test consumer response and behaviour. This research employs the methods of questionnaires, market analysis, focus groups and interviews. Its purpose is to determine consumers' intentions to purchase a service, attitudes towards new and existing services, price sensitivity and cross service elasticities. Market research helps make decisions concerning which new services should be developed. A combination of the qualitative and quantitative phases of market research can be used in the initial stages of forecasting the demand for a new service.д Ј*дŒа H аС СThe design of market research considers a sampling frame, customer/market stratification, the selection of a statistically random sample and the correction of results for nonР-Рresponse bias. The sample can be drawn from the entire market or from subsegments of the market. In sampling different market segments, factors which characterize the segments must be alike with respect to consumer behaviour (small intragroup variance) and should differ as much as possible from other segments (large intergroup variance); each segment is homogeneous while different segments are heterogeneous. а H аС СThe market research may be useful in forecasting existing services or the penetration of new services. The research may be used in forecasting novel services or any service which has no historical series of demand data. It is important that potential consumers be given a complete description of the new service, including the terms and conditions which would accompany its provisioning. It is also important to ask the surveyees whether they would purchase the new service under a variety of illustrative tariff structures and levels. This aspect of market research will aid in redimensioning the demand upon final determination of the tariff structure and determining the customers' initial price sensitivity. аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС‚У У5С  Сб cмˆ4 PŽТ бForecasting proceduresЦЦ аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФ Ф5.1Тh  ТУУGeneralЦЦ ФФС СThe absence of historical data is the fundamental difference between forecasting new services and forecasting existing services. The forecast methodology is dependent on the base data. For example, for a service that is planned but has not been introduced, market research survey data can be used. If the service is already in existence in some countries, forecasting procedures for its introduction to a new country will involve historical data on other countries, its application to the new country and comparison of characteristics between countries. 5.2Тh  ТУУSampling and questionnaire designЦЦ а H аФФС СThe forecasting procedure for novel services based on market research is made up of five consecutive steps. The first of these consists in defining the scope of the study. а H аС СThe second step involves the definition and selection of a sample from the population, where the population includes all potential customers which can be identified by qualitative market research developed through interviews at focus groups. The research can use stratified samples which involves grouping the population into homogeneous segments (or strata) and then sampling within each strata. Stratification prevents the disproportionate representation of some parts of the population that can result by chance with simple random sampling. The sample can be structured to include specified numbers of respondents having characteristics that are known, or believed, to affect the subject of the research. Examples of customer characteristics would be socioР-Рeconomic background and type of business. а H аС СThe third step is the questionnaire design. A tradeР-Рoff exists between obtaining as much information as practical and limiting the questionnaire to a reasonable length, as determined by the surveyor. Most questionnaires have three basic sections: а H аТа ТТ№ ТС€ С1)СpСqualifying questions to determine if a knowledgeable person has been contacted;ЦЦ а H аТа ТТ№ ТС€ С2)СpСbasic questions including all questions which constitute the body of the questionnaire;ЦЦ а Hx аТа ТТ№ ТС€ С3)СpСclassification questions collecting background on demographic information.ЦЦ а H аС СThe fourth step involves the implementation of the research Р-Р the actual surveying portion. Professional interviewers, or firms specializing in market research should be employed for interviewing. С СThe fifth and final step is the tabulation and analysis of the survey data. РSР 5.3Р-Р5.7 describe this process in detail. 5.3Тh  ТУУConversion ratios for the sampleЦЦ а H аФФС СConversion ratios are used in estimating the proportion of respondents expressing an interest in the service who will eventually subscribe. а H аС СThe analysis of the market research data based on a sample survey, where a stratified sample is drawn across market segments, for a service that is newly introduced or is planned, is discussed below: С СLet а H№ аТа ТТ№ ТС€ СУУXФФУУ1УУiФФФФСpС=Си Сthe proportion of firms in market segmentУУ iФФ that are very interested in the service.ЦЦ а H аТа ТТ№ ТС€ СУУXФФУУ2УУiФФФФСpС=Си Сthe proportion of firms in market segmentУУ iФФ that are interested in the service.ЦЦ а H аТа ТТ№ ТС€ СУУXФФУУ3УУiФФФФСpС=Си Сthe proportion of firms in market segmentУУ iФФ that are not interested in the service.ЦЦ а H аТа ТТ№ ТС€ СУУXФФУУ4УУiФФФФСpС=Си Сthe proportion of firms in market segmentУУ iФФ that cannot decide whether they are interested or not.ЦЦ а H№ аС СThe above example has 4 categories of responses. Greater of fewer categories may be used depending on the design of the questionnaire. С СNotice that аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8Сeq \i\su(j, , ) XƒУУjiФФФФ = 1, аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаwhereУУ jФФ = the index of categories of responses. а H аС СMarket research firms sometimes determine conversion ratios for selected product/service types. Conversion ratios depend on the nature of the service, the type of respondents, and the questionnaire and its implementation. Conversion ratios applied to the sample will estimate the expected proportion of firmsУУ in the surveyФФ that will eventually subscribe, over the planning period. For studies related to the estimation of conversion ratios, refer to [1], [3] and [5]. С СThen, а H аТа ТТ№ ТТhpТТhи ТС€pСС€СС€ СУУcФФУУ1ФФУУXФФУУ1УУiФФФФСи С=СЈ Сthe proportion of firms in market segmentУУ iФФ that expressed a strong interest and are expected to subscribe.ЦЦ а H аТа ТТ№ ТТhpТТhи ТС€pСС€СС€ СУУcФФУУ2ФФУУXФФУУ2УУiФФФФСи С=СЈ Сthe proportion of firms in market segmentУУ iФФ that expressed an interest and are expected to subscribe.ЦЦ а H аТа ТТ№ ТТhpТТhи ТС€pСС€СС€ СУУcФФУУ3ФФУУXФФУУ3УУiФФФФСи С=СЈ Сthe proportion of firms in market segmentУУ iФФ that expressed no interest but are expected to subscribe.ЦЦ а H аТа ТТ№ ТС€ СУУcФФУУ4ФФУУXФФУУ4УУiФФФФСи С=СЈ Сthe proportion of undecided firms in market segmentУУ iФФ that are expected to subscribe.ЦЦ Та ТТ№ ТС€ СwhereУУ cУУjФФФФСЈ С=С Сconversion ratio for responseУУ jФФ.ЦЦ а H аС СThe proportion of firms in market segmentУУ iФФ,УУ PУУiФФФФ, that are expected to subscribe to the service, equals аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8Сeq PƒУУiФФФФ = \i\su(УУjФФ=1,4,УУcУУjФФ XУУjiФФФФ)СH8А"FС(5ƒР-Р1) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаС СThe conversion ratio is based on the assumption that there is a 100% market awareness. That is, all surveyees are fully informed of the service availability, use, tariffs, technical parameters, etc.УУ PУУiФФФФ, therefore, can be interpreted as the longР-Рrun proportion of firms in market segmentУУ iФФ that are expected to subscribe to the service at some future time period,УУ TФФ. а H аС СTwo issues arise in the estimation of the proportion of customers that subscribe to the service: а H аТа ТТ№ ТС€ С1)СpСwhileУУ PУУiФФФФ refers to the sample surveyed, the results need to be extrapolated to represent the population.ЦЦ а H аТа ТТ№ ТС€ С2)СpСУУPУУiФФФФ is the longР-Рrun (maximum) proportion of firms expected to subscribe. We are interested in predicting no just the eventual number of subscribers but, also, those at intermediate time periods before the service reaches a saturation point.ЦЦ а HH а5.4Тh  ТУУExtrapolation from sample to populationЦЦ а H аФФС СTo extrapolate the data from the sample to represent the population, let а H аС СУУNУУiФФФФ =Си Сsize of market segmentУУ iФФ (measured for example, by the number of firms in market segmentУУ iФФ) С СThenУУ SУУiФФФФ, the expected number of subscribers in the planning horizon, equals: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8%СSƒУУiФФФФ =УУ PУУiФФNУУiСH.А"FСƒФФФФ(5Р-Р2) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬа5.5Тh  ТУУMarket penetration over timeЦЦ а H аФФС СTo determine the expected number of subscribers at various points in time before the service reaches maturity, let а H аС СУУpУУitФФФФ = the proportion of firms in market segmentУУ iФФ that are expected to subscribe at timeУУ tФФ. С СClearly, С СУУpУУitФФФФ <УУ PУУiФФФФ andС  СУУpУУitФФФФ Љ>УУ PУУiФФФФ as УУtФФ Љ>УУ TФФ С СThe relation betweenУУ pУУitФФФФ andУУ PУУiФФФФ can be explicitly defined as: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚С СС pССШ8#СpƒУУitФФ = aУУitФФ . PУУiСH1А"FСƒФФ(5Р-Р3) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаУУaУУitФФФФ is a penetration function, reflecting changing market awareness andд ё,д acceptance of the service over time, in market segmentУУ iФФ. An appropriate functional form forУУ aУУitФФФФ should be bounded in the interval (0,1). С СAs an example, letУУ aУУitФФФФ be a logistic function: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8СaƒУУitФФФФ = eq \f( 1, 1 +УУ eУУб cмˆ4 PŽТ бbitб cмˆ4 PŽТ бФФФФ)СH7А"FС(5ƒР-Р4) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаУУbУУiФФФФ 0 is the speed with whichУУ pУУitФФФФ approachesУУ PУУiФФФФ in market segmentУУ iФФ, as illustrated in Figure 1/E.508. а H аС СFor other examples of nonР-Рlinear penetration functions, refer to the Annex A. ‚Ср KСб cмˆ4 PŽТ бFigure 1/E.508 Љ T0201030Љ87 б cмˆ4 PŽТ б а H аС СThe introduction of a new service will usually differ according to the market segment. The rate of penetration may be expressed as a function of time, and the speed of adjustment (УУbУУiФФФФ) may vary across segments. Lower absolute values ofУУ bУУiФФФФ, for the logistic function will imply faster rates of penetration. С СWhile the form of the penetration function relating the rate of penetration to time is the same for all segments, the parameterУУ bУУiФФФФ varies across segments, being greater in segments with a later introduction of the new service. а H аС СLetУУ tФФУУ0УУiФФФФСP С=СЈ Сtime period of introduction of service in market segmentУУ iФФ. а H аС СThen,УУ tФФ Р-РУУ tФФУУ0УУiФФФФС С=С!X%Сtime period elapsed since service was introduced in market segmentУУ iФФ. С СIn the diagramatic illustration, of Figure 2/E.508, the service has achieved the same level of market penetrationУУ aФФУУ0ФФ, inУУ tУУCФФФФ periods after its introduction in marketУУ CФФ as it did inУУ tУУAФФФФ periods after its introduction in market segmentУУ AФФ. Later introductions may not necessarily lead to faster rates of penetration across segments. However, within the same market segment, across countries with similar characteristics, such an expectation is reasonable. ‚Ср KСб cмˆ4 PŽТ бFigure 2/E.508 Љ T0201350Љ88 б cмˆ4 PŽТ б аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС5.6С   Сб cмˆ4 PŽТ бУУGrowth of market segment over timeЦЦ а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФФС СThe above discussion has accounted for gradual market penetration of the new service, by allowingУУ pУУitФФФФ to adjust toУУ PУУiФФФФ over time. The same argument can be extended to the size of market segmentУУ iФФ over time. С СLetУУ nУУitФФФФ = size of market segmentУУ iФФ at timeУУ tФФ. а H аС СThen, the expected number of subscribers at timeУУ tФФ in market segmentУУ iФФ, equals: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚С СС pССШ8 СsƒУУitФФ = aУУitФФ . pУУitФФ . nУУitСH5А"FСƒФФ(5Р-Р5) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаand С СУУeq SУУtФФФФ =УУ \i\su(iФФ, , УУSУУitФФ ФФ)УУ ФФ= expected number of subscribers across all market segments at timeУУ tФФ. 5.7Тh  ТУУQuantities forecastedЦЦ а H аФФС СThe above procedure forecasts the expected number of customers for a new service within a country. Other quantities of interest may include lines, minutes, messages, revenue, packets, kilobits, etc. The most straightforward forecasting method for some of these quantities is to assume constant relationships such as: а H аТа ТТ№ ТС€ Сexpected access linesС"X%С=С&А*С(average access lines) РxР expected number of subscribersЦЦ а H аТа ТТ№ ТС€ Сexpected minutesС С=С!X%С(average use per line) РxР expected access linesЦЦ а H аТа ТТ№ ТС€ Сexpected messagesС С=С!X%Сexpected minutes/(average length of conversation)ЦЦ а H аТа ТТ№ ТС€ Сexpected revenueС С=С!X%С(average rate per minute) РxР expected minutesЦЦ а H аС СThe constants, appearing in parentheses, above, can be determined through 1) the process of market research, or 2) past trends in similar services. аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС5.8С   Сб cмˆ4 PŽТ бУУForecasting with historical data: application analysisЦЦ а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФФС СAfter a new service has been introduced, historical data can be analyzed to forecast demand for expanded availability to other countries. Development of a new service will follow trends based on applications, such as data transmission, travel reservations, intracompany communications, and supplier contact. Applications of a service vary widely and no single variable may be an adequate indicator of total demand. С СThe following procedure links demand to country characteristics for forecasting expanded availability of a new service to other countries. С СLetУУ DФФ = (УУDУУiФФФФ,УУ DФФУУ2ФФ, . . . . . .,УУ DУУnФФФФ)` а H аrepresent a vector of countryР-Рspecific annual demand for the service acrossУУ nФФ countries, where the service currently exists. LetУУ CФФ = matrix ofУУ mФФ characteristics relating to each of theУУ nФФ countries that are reasonable explanatory variables of demand. The components ofУУ mФФ would vary depending on the nature of the service and its application. а H аС СSome essential components ofУУ mФФ would be the price of the service (or an index representing its price) and some proxy for market awareness. As discussed in earlier sections, market awareness is one of the key determinants of the rate of market penetration of the service. Reasonable proxies would be advertising expenditures and time (measured asУУ tФФ* =УУ tФФ Р-РУУ tФФУУ0ФФ) whereУУ tФФ* would measure time elapsed since the service was first introduced at timeУУ tФФУУ0ФФ. Market awareness can be characterized as some nonР-Рlinear function ofУУ tФФ*, as presented in РSР 5.5. Other components ofУУ mФФ may include socioР-Рeconomic characteristics of the customers, market size and location of customers. С СThe model that is estimated is: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8%СDƒФФ =УУ CФФРР +УУ uСH/А"FСƒФФ(5Р-Р6) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаwhere Та ТТ№ ТС€ СУУCФФ is a (УУnФФ РxРУУ mФФ) matrix of country characteristicsЦЦ Та ТТ№ ТС€ СУУDФФ is a (УУnФФ РxР 1) vector of demandЦЦ а H аТа ТТ№ ТС€ СРР is a (УУmФФ РxР 1) vector of coefficients corresponding to each of theУУ mФФ characteristicsЦЦ Та ТТ№ ТС€ СУУuФФ = (УУnФФ РxР 1) vector of error termsЦЦ а HH аС СThe estimated regression is: аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8Сeq \o(\s\up4(^),D)ƒФФ =УУ C\o(\s\up4(^),ФФРР)СH>А"FС(5ƒР-Р7) а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаС СTraditional methods of estimating regressions will be applied. Equation (5Р-Р7) can be used for predicting demand for any country where the service is being newly introduced, as long as elements of the matrixУУ CФФ are available. 5.9Тh  ТУУForecasting with limited informationЦЦ ФФС СIn the extreme case where no market research data is available (or is uneconomical given resource constraints), or country characteristics that affect demand are not easily available or quantifiable, other methods of forecasting need to be devised. а H аС СFor example, to forecast the demand for a new international private line service using digital technology, the following elements should be taken into account in the development of reasonable estimates of the expected number of lines: Та ТТ№ ТС€ Сa)СpСdiscussions with foreign telephone companies,ЦЦ а H аТа ТТ№ ТС€ Сb)СpСdiscussions with very large potential customers regarding their future needs,ЦЦ Та ТТ№ ТС€ Сc)СpСservice inquiries from customers,ЦЦ Та ТТ№ ТС€ Сd)СpСcustomer letters of intent, andЦЦ Та ТТ№ ТС€ Сe)СpСany other similar qualitative information.ЦЦ а HH ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС‚У У6С  Сб cмˆ4 PŽТ бForecast tests and adjustmentsЦЦ аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФ Ф6.1Тh  ТУУGeneralЦЦ а H аФФС СForecast tests and adjustments are dependent on the methodology applied. For example, in the case of a market research based forecast, it is important to track the forecast of market size, awareness and rate of penetration over time and to adjust forecasts accordingly. However, for an applicationР-Рbased methodology, traditional tests and adjustments applicable to regression methods will be employed, as discussed below. аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТX  ТТX јТС€  СС€ HС6.2С   Сб cмˆ4 PŽТ бУУMarket research based analysisЦЦ а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФФС СThis section discusses adjustments to forecasts based on the methodology described in РSРS 5.2 to 5.8. The methodology was based on quantification of responses from a sample survey. С СThe forecast was done in two parts: а H аТа ТТ№ ТС€ Сa)СpСextrapolating the sample to the population, using market size,УУ NУУiФФФФ;д ё,дЦЦŒа H аТа ТТ№ ТС€ Сb)СpСallowing for gradual market penetration (awareness),УУ aУУitФФФФ of the new service over time.ЦЦ а H аС СThe values attributed toУУ nУУitФФФФ (which represents the size of market segmentУУ iФФ at timeУУ tФФ) andУУ aУУitФФФФ can be tracked over time and forecast adjustments made in the following manner: а H аТа ТТ№ ТС€ Сa)СpСAs an example forУУ nУУiiФФФФ, the segments could be categorized as travel or financial services. The size of the segment would be the number of tourists, and the number of large banks. Historical data, where available, on these units of measurement can be used to forecast their sizes at any point of time in the future. Where history is not available, reasonable growth factors can be developed through subject matter experts and past experiences. The forecast ofУУ nУУitФФФФ should be tracked against actual measured values and adjusted for large deviations.ЦЦ а H аТа ТТ№ ТС€ Сb)СpСForУУ aУУitФФФФ, testing with only a few observations since the introduction of the service is more difficult.ЦЦ а HH аС СС СGiven that, аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚УУС СС pССШ8 СaƒУУitФФФФ = eq \f(УУ pУУitФФФФ,УУPУУiФФФФ)СH4А"FС(6ƒР-Р1) а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаТа ТТ№ ТandУУ PУУiФФФФ is assumed fixed (in the long run), testingУУ aУУitФФФФ is equivalent to testingУУ pУУitФФФФ.УУ pУУitФФФФ can be tracked by observing the proportion of respondents that actually subscribe to the service at timeУУ tФФ. This assumes the need to track the same individuals who were originally in the survey, as is customary in a panel survey. Panel data is collected through sample surveys of crossР-Рsections of the same individuals, over time. This method is commonly used for household socioР-Рeconomic surveys. Having observedУУ pУУitФФФФ for a new period, values ofУУ aУУitФФФФ can be plotted against time to study the nature of the penetration function,УУ aУУitФФФФ, and the most appropriate functional form that fits the data should be chosen. At very early stages of service introduction, traditional functional forms for market penetration, such as a logistic function (as illustrated in the example in РSР 5.5), will be a reasonable form to assume. Other variations of the functional form depicting market penetration would be the Gompertz or Gauss growth curves. The restriction is that the penetration function should be bounded in the interval (0,1). See Annex A for an algebraic depiction of functional forms.ЦЦ а H аС СThere are various statistical forms that may be chosen as representations for the penetration function. The appropriate functional form should be based on some theoretical based information such as the expected nature of penetration of the specific service over time. а H аС СContinuous tracking ofУУ nУУitФФФФ,УУ pУУitФФФФ andУУ aУУitФФФФ over time will enable adjustments to these values whenever necessary and enable greater confidence in the forecasts. 6.3Тh  ТУУApplication based analysisЦЦ ФФС СThe application based analysis is a regression based approach and traditional forecast tests for a regression model will apply. For instance, hypothesis tests on each of the explanatory variables included in the model will be а H аnecessary. Corrections may be needed for heteroР-Рelasticity, serial correlation and multicollinearity, when suspect. The methodology for performing such tests are described in most econometrics text books. In particular, references [2] and [4] can be used as guidelines. Recommendation E.507 also discusses these corrections. а H аС СAdjustments need to be made for variables that should be included in the regression model but are not easily quantifiable. For example, market awareness that results from advertising and promotional campaigns plays an important role in the growth of a new service, but data on such expenditures or the associated awareness may not be readily available. Some international services are targeted towards international travelers, and fluctuations in exchange rates will be a determining factor. Such variables, while not impossible to measure, may be expensive to acquire. However, expectations of future trends in such variables can enable the forecaster to arrive at some reasonable estimates of their impact on demand. Unexpected occurrences such as political turmoil and natural disasters in particular countries will also necessitate post forecast adjustments based upon managerial judgement. С СAnother important adjustment that may be necessary is the expected competition from other carriers offering similar or substitutable services. Competitor prices, if available, may be used as explanatory variables within the model and allow the measurement of a crossР-Рprice impact. In most situations, it is difficult to obtain competitor prices. In such cases, other methods of calculating competitor market shares need to be developed. а H аС СRegardless of forecasting methodology, the final forecasts will have to be reviewed by management responsible for planning the service as well as by network engineers in order to assess the feasibility both from a planning implementation and from a technical point of view. ‚Ср VСб cмˆ4 PŽТ бANNEX A Ср MСб cмˆ4 PŽТ б(to Recommendation E.508) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџH јP Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаСр GСб cмˆ4 PŽТ бУ УPenetration functions (growth curves) а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаб cмˆ4 PŽТ бФ ФС СSome examples of nonР-Рlinear penetration functions are illustrated below: A.1Тh  ТLogistic curveУУЦЦ аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚С СС pССШ8 СaƒУУitФФФФ = a / {1 + eУУб cмˆ4 PŽТ бР-РУУbtб cмˆ4 PŽТ бФФФФ}СH4А"FС(AƒР-Р1) а H ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаС СFor a = 1, the curve is bounded in the interval (0,1). ChangingУУ bФФ will alter the steepness of the curve. The higher the value ofУУ bФФ, the faster the rate of penetration. This curve is SР-Рshaped and is symmetrical about its point of inflection, the latter being where; аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚С СС pССШ8 Сeq \f(dƒб cмˆ4 PŽТ бУУ2ФФб cмˆ4 PŽТ бУУaУУitФФФФ,dУУtФФУУб cмˆ4 PŽТ б2б cмˆ4 PŽТ бФФ) = 0СH4А"FС(AƒР-Р2) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаA.2Тh  ТGompertz curveУУЦЦ аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚С СС pССШ8Сeq aƒУУitФФФФ = a exp eq \b\bc\{(Р-РУУbФФeУУб cмˆ4 PŽТ бР-РУУktб cмˆ4 PŽТ бФФФФ)СH<А"FС(AƒР-Р3) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаС СAsУУ tФФ Љ> УУ aУУitФФФФ Љ> a, the limiting growth. а H аС СHoldingУУ kФФ = 1 and a = 1, higher values ofУУ bФФ will imply slower rates of penetration. This curve is also SР-Рshaped like the logistic curve, but is not symmetrical about its inflection point. а H аС СWhenУУ tФФ = 0, thenУУ aУУitФФФФ = aeУУб cмˆ4 PŽТ бР-РУУbб cмˆ4 PŽТ бФФФФ, which is the initial rate of penetration. Та ТA.3СpСУУGauss curveЦЦ а HH ааЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHp8А"(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ Ьа‚С СС pССШ8СaƒУУitФФФФ = a eq \b(1 Р-Р eУУб cмˆ4 PŽТ бР-РУУbtФФ2ФФб cмˆ4 PŽТ б)СH7А"FС(AƒР-Р4) аЬџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџHpи P Ј XА`ИhР!(#џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџЬаС СAsУУ tФФ Љ> , thenУУ aУУб cмˆ4 PŽТ бitб cмˆ4 PŽТ бФФФФ Љ> a С СAsУУ tФФ Љ> 0, thenУУ aУУб cмˆ4 PŽТ бitб cмˆ4 PŽТ бФФФФ Љ> 0. С СChoosing a = 1, the curve is bounded in the interval (0,1). ‚У УС СReferencesФ Ф а H а[1]Тh  ТAXELROD (J. N.): Attitude measures that predict purchase,УУ Journal of Advertising ResearchФФ, Vol. 8, No. 1, pp. 3Р-Р17, New York, March 1968.ЦЦ а H а[2]Тh  ТJOHNSTON (J.): Econometric methods, Second Edition,УУ McGrawР-РHillФФ, New York, 1972.ЦЦ а H а[3]Тh  ТKALWANI (M. U.), SILK, (A. J.): On the reliability and predictive validity of purchase intention measures,УУ Marketing ScienceФФ, Vol. 1, No. 3, pp. 243Р-Р286, Providence, RI, Summer 1982.ЦЦ а H а[4]Тh  ТKMENTA (J.): Elements of econometrics,УУ Macmillan Publishing Co.ФФ, New York, 1971.ЦЦ а H а[5]Тh  ТMORRISON (D. G.): Purchase intentions and purchase behavior,УУ Journal of MarketingФФ, Vol. 43, pp. 65Р-Р74, Chicago, Ill., Spring 1979.ЦЦ ‚У УС СBibliographyФ Ф BENР-РAKIVA (M.) and LERMAN (S. R.): Discrete choice analysis. а H аDRAPER (N.) and SMITH (H.): Applied regression analysis, Second Edition,УУ John Wiley & SonsФФ, New York, 1981.