The 3 F 2 with Complex Parameters as Generating Function of Discrete Distribution

A new discrete family of probability distributions that are generated by the ₃ F ₂ function with complex parameters is presented. Some of the properties of this new family are studied as well as methods of estimation for its parameters. It affords considerable flexibility of shape which turns the distribution into an appropriate candidate for modeling data that cannot be adequately fitted by classical families with fewer parameters. Finally, three examples in the fields of Agriculture and Education are included in order to show the versatility and utility of this distribution.     

A New Generalized Exponential Geometric Distribution

In this article, another version of the generalized exponential geometric distribution different to that of Silva et al. (2010 Silva , R. B. , Barreto-Souza , W. , Cordeiro , G. M. ( 2010 ). A new distribution with decreasing, increasing and upside-down bathtub failure rate. Computat. Statist. Data Anal. 54: 935–944 . [Google Scholar]) is proposed. This new three-parameter lifetime distribution with decreasing, increasing, and bathtub failure rate function is created by compounding the generalized exponential distribution of Gupta and Kundu (1999 Gupta , R. D. , Kundu , D. ( 1999 ). Generalized exponential distributions . Austral. NZ J. Statist. 41 ( 2 ): 173 – 188 .[Crossref], [Web of Science ®] , [Google Scholar]) with a geometric distribution. Some basic distributional properties, moment-generating function, rth moment, and Rényi entropy of the new distribution are studied. The model parameters are estimated by the maximum likelihood method and the asymptotic distribution of estimators is discussed. Finally, an application of the new distribution is illustrated using the two real data sets.     

The analysis of some biological data

This paper considers the building of stochastic models and the related analysis of discrete data in two biological problems, The first arises from the reproduction of yeast cells, while the secondis concerned with the aggregation of nucleoli. Galton-Watson and aggregation models are constructed for the respective processes and their goodness of fit to the data tested     

The questions of fit in the gregor mendel controversy

Ever since R. A. Fisher published his 1936 article , "Has Mendel's Work Been Rediscovered?", historians of both biclogy and statistics have been fascinated by the surprisingly high conformity between Gregor (Johann) Mendel's observed and expected ratios in his famous experiments with peas. Fisher's calculatftl x² statistic of the experiments, taken as a whole, suggested that results on a par or better than those Mendel reported coultl only be expected to occur about three times in every 100,000 attempts. The ensuing controversy as to whether or not the good Father "sophisticated" his data has continued to this very day. In recent years the controversy has focused upon the more technical question of what underlying genetic arrangement Mendel actually studied.

The statistical issues of the controversy are exam:.led in am historical and comparative perspective. The changes the controversy has gone through are evaluated, and the nature of its current, more biological, status is briefly discussed.     

A unified approach to estimating parameters in some generalized poission distributions

A family of distributions labelled as Poisson v Katz is formulated, which includes, as particular or limiting cases, the Negative Binomial, Neyman Type A, Poisson v Pascal, and Poisson v Binomial. Thus, while analyzing data, estimating the parameters in the Poisson v Katz family obviates the necessity of having to choose from among the particular or limiting cases. In this article minimum chi-square estimators are presented and their asymptotic relative efficiency obtained. An example is presented to illustrate the procedure     

BIVARIATE DISTRIBUTION WITH TRUNCATED POISSON MARGINAL DISTRIBUTIONS

ABSTRACT

A bivariate distribution, whose marginal distributions are truncated Poisson distributions, is developed as a product of truncated Poisson distributions and a multiplicative factor. The multiplicative factor takes into account the correlation, either positive or negative, between the two random variables. The distributional properties of this model are studied and the model is fitted to a real life bivariate data.     

Basu's Lemma and Goodness-of-Fit Tests

In this paper we develop a technique that is useful in goodness of fit problems with nuisance location and scale parameters. Using Basu's lemma, we transform the sample so that it is independent of the nuisance parameters. The technique will be illustrated by several examples, a discussion of the efficiency of the proposed procedure, and some concluding remarks will given.     

Use of the Correlation Coefficient with Normal Probability Plots

The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position p_i = (i - .375)/(n + .25) yields a competitive regression test of fit for normality.     

Spectral goodness of fit for network models

We introduce a new statistic, ‘spectral goodness of fit’ (SGOF) to measure how well a network model explains the structure of the pattern of ties in an observed network. SGOF provides a measure of fit analogous to the standard R² in linear regression. Additionally, as it takes advantage of the properties of the spectrum of the graph Laplacian, it is suitable for comparing network models of diverse functional forms, including both fitted statistical models and algorithmic generative models of networks. After introducing, defining, and providing guidance for interpreting SGOF, we illustrate the properties of the statistic with a number of examples and comparisons to existing techniques. We show that such a spectral approach to assessing model fit fills gaps left by earlier methods and can be widely applied.