APPROXIMATE METHODS FOR DETERMINATION OF OPTIMUM STRATIFICATION BOUNDARY POINTS FOR BETA, GAMMA, AND PARETO DISTRIBUTIONS

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dc.contributor.authorBELLO, RAZAQ
dc.date.accessioned2014-02-11T11:02:33Z
dc.date.available2014-02-11T11:02:33Z
dc.date.issued1986-08
dc.descriptionA thesis submitted to the Postgraduate School, Ahmadu Bello University, Zaria, in partial fulfilment of the requirements for the depree of Doctor of Philosophy in Statistics.en_US
dc.description.abstractStratification is the division of a heterogeneous population into relatively homogeneous sub-populations. Using Stratification we can usually improve the efficiency of the estimate of mean of the population. Stratification may be inevitable in terms of administrative convenience. Stratification of Hospitals may be by bed capacity, of schools by enrolment, of business concern by volume of sales, of industrial plants by employment and of voluntary organisation by membership. te finite nopulations encounte in practice are all discontinuous. If the populations are sufficiently large, they can very often be approximated by some standard continuous distributions. Thus tables of strata boundaries for these standard distributions can profitably be utilized for the stratification of an. actual population. Under Tchunrow-Neyman allocation, Dalenius (1950) derived equations for the strata boundaries yhwhich minimize the variance of th estimated population mean. But these equations are troublesome to solve. A number of approximate methods that could quickly solve the Dalenius equations have been proposed by several authors. These approximate methods are: (i) Cum /f Method (ii) Durbin's Method (i i i) Ekman's Method (iv) Equal Range Method (v) Equal Sized Strata Method (vi) Equalization of Strata Total Method. The author has developed computational procedures for Parens the determination of s t r a t a boundaries for Beta and Gamma * Distributions with various values of the parameters using the above methods except (iii). The methods are compared using the variance of the stratified sample mean. The best boundaries are those that give the least variance of the stratified sample mean. All the methods construct strata boundaries quickly fox- Beta Distribution. For Gamma Distribution, only the cum gammamma method constructs strata boundaries quickly. For ParetO distribution with parameter 0 all the methods consider lead to a very substantial reduction in variance of the estimate of the mean of population except the equal ran method, and all the method construct the strata boundaries quickly. We conclude that the cum gamma of f method is the best method, of constructing strata boundaries among those considered in this study. A critical examination of the behavior of the variance as a function of the parameters p and a of the Beta distribution and the number of strata k has shown that for Beta distribution the variance decreases by about 10%, for a unit increase in a when 1 _< p -< 4 and k are fixed; while the variance increases and then decreases when p _> 5. We have the sane conclusion when p and q are interchanged. For the Gamma distribution with parameters beta and p it is observed that for fixed k the variances increase as one of the numbers v or 8 is increased while the other remains constant.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/1165
dc.language.isoenen_US
dc.subjectAPPROXIMATE METHODS,en_US
dc.subjectDETERMINATION,en_US
dc.subjectOPTIMUM,en_US
dc.subjectSTRATIFICATION,en_US
dc.subjectBOUNDARY POINTS,en_US
dc.subjectBETAen_US
dc.subjectGAMMAen_US
dc.subjectPARETO DISTRIBUTIONSen_US
dc.titleAPPROXIMATE METHODS FOR DETERMINATION OF OPTIMUM STRATIFICATION BOUNDARY POINTS FOR BETA, GAMMA, AND PARETO DISTRIBUTIONSen_US
dc.typeThesisen_US
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