Theorizing Probability Distribution in Applied Statistics

Journal of University of Shanghai for Science and Technology, 2021

This is a speculation of binomial appropriation with n and two additional boundaries and there is no supposition in regards to the autonomy and furthermore steady likelihood of preliminaries that have been presented. The likelihood of a triumph during a preliminary is constantly considered as a straight capacity of all the past number of victories. The dissemination for the equivalent has been found to give nearer results to a wide range of discrete information or datasets. The Consul and Jain’s (1973) summed up Poisson conveyance as the restricting case for something similar. The end or general mean of this dissemination has been found and its conduct with the changing upsides of the boundaries is analyzed and examined.

K Y PUBLICATION , 2021

The Poisson distribution is a discrete distribution and is characterized by only one parameter namely " ", the mean number of successes per given unit of time and space. In literature, while there are reports about the size of the that should be acceptable for the initiation of the Normal approximation to the Poisson distribution, there is hardly any mention on the role of the size of the sample in the Normal approximation. In the present study, therefore an attempt is made to check the role of the sample size, if any, in Normal approximation of the Poisson distribution? Two random samples of Poisson distribution are generated for each of the selected (2,3,5 and 10) value and for the sample size (50, 100 and 200). Correspondingly, the Normal sample is also generated. It is known that if X follows the Poisson distribution with mean = , then Z = − √ is assumed to follow the standard Normal variate. To assess the validation of the Normal approximation, the   approach is utilized. In general, for each (2,3,5 and 10) value and the sample size (50,100 and 200), the Normal approximation to the Poisson distribution is found to be valid. The study has brought out clearly that for the sample size as low as 50 and =2, the Normal approximation to the Poisson distribution can be carried out.

The Encyclopedia of Archaeological Sciences, S. L. López Varela (Ed.), 2018

Probability distributions are important tools for assessing the probability of the outcomes that occur. In particular, archaeologists have used the binomial and the Poisson distributions in order to model the likelihood of discrete archaeological phenomena.This section introduces these two methods and shows practical examples where they can be applied to archaeological contexts. The two distributions are, therefore, comparatively described and evaluated on their similarities and differences. The binomial distribution models the probability of “successes” and “failures” in a fixed number of trials. Instead, the Poisson distribution counts the occurrences occurring in a given unit of time or space with no fixed cutoff.

2013

This thesis was written during my two-year term, between July 1954 and July 1956, as a Research Scholar of the Australian National University. This thesis is divided into two parts, the first consisting of chapters 1, 2, 3 on curve-fitting and the evaluation of certain integrals, and the second of chapters 4 and 5 on the testing of various unconnected hypotheses. The work in the first chapter

2019

A new distribution called Ristić and Balakrishnan Lindley-Poisson (RBLP) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Lindley-Poisson, RB-Lindley and Lindley distributions. Some statistical properties of the proposed distribution including hazard rate function, moments and conditional moments are presented. Mean deviations, Lorenz and Bonferroni curves, Rényi entropy and distribution of the order statistics are given. Maximum likelihood estimation technique is used to estimate the model parameters. Finally, application of the model to a real dataset is presented to illustrate the usefulness of the proposed distribution.

Journal of Statistical Distributions and Applications, 2014

Afrika Statistika, 2018

A new distribution called Ristić and Balakrishnan Lindley-Poisson (RB-LP) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Lindley-Poisson, RB-Lindley and Lindley distributions. Some statistical properties of the proposed distribution including hazard rate function, moments and conditional moments are presented. Mean deviations, Lorenz and Bonferroni curves, Rényi entropy and distribution of the order statistics are given. Maximum likelihood estimation technique is used to estimate the model parameters. Finally, application of the model to a real dataset is presented to illustrate the usefulness of the proposed distribution.

Journal of Modern Applied Statistical Methods, 2009

This article reviews some useful discrete models and compares their performance in terms of the high frequency of zeroes, which is observed in many discrete data (e.g., motor crash, earthquake, strike data, etc.). A simulation study is conducted to determine how commonly used discrete models (such as the binomial, Poisson, negative binomial, zero-inflated and zero-truncated models) behave if excess zeroes are present in the data. Results indicate that the negative binomial model and the ZIP model are better able to capture the effect of excess zeroes. Some real-life environmental data are used to illustrate the performance of the proposed models.