Statistical Inference in Contagious Distributions with Emphasis on Neyman Type A Distribution | ||
| The Egyptian Statistical Journal | ||
| Article 3, Volume 28, Issue 2, December 1984, Pages 57-75 | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.1984.316604 | ||
| Authors | ||
| Magdy Khedr; M. Elmoslimany | ||
| Abstract | ||
| Several distributions have been proposed for fitting to a large class of biological and entomological data which have been characterized as being contagious. Many researchers have worked on fitting the contagious distributions to several kinds of contagious data collected in U.S.A. The idea of fitting the biological and entomological data, i.e, contagious data is general using contagious distributions have not been used by many researchers including those in Egypt. The basic purpose of this paper is to give an idea about the types of contagious data and contagious distributions used in fitting these data and the major reason for the disability of using the simple distributions such as Poisson, binomial and logarithmic for fitting contagious data. As a special case, Neyman Type A distribution is considered as one of the contagious distributions and some preliminary investigations such as its probability generating function (p.g.f) and the recursion formula for the probabilities have been discussed. Since obtaining the maximum likelihood estimates is extremely difficult for this and other contagious distributions, the moment estimates used as an initial estimate in solving the likelihood equations iteratively. Finally, the graph of the likelihood contours for one set of data is presented. | ||
| Keywords | ||
| Contagious Distributions; Fitting Distributions; Likelihood Equations; Moment Estimates; Neyman Type A Distribution; Probability Generating Function; Recursion Formula | ||
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