The main aim of this article is to characterize and investigate the three parameter exponentiated exponential Poisson probability distribution EEP(α, β, λ) by giving explicit closed form expressions for its characteristic function φξ(t) and moment generating function Mξ(t), and finally, to show that the existing series and integral form expressions for positive integer order moments Eξ , ν ∈ N ...

A quality of centroid-based clustering is highly dependent on initialization. In the article we propose initialization based on the probability of finding objects, which could represent individual clusters. We present results of experiments which compare the quality of clustering obtained by k-means algorithm and by selected methods for fuzzy clustering: FCM (fuzzy c-means), PCA (possibilistic ...

In such situations we are often interested in whether the events occur randomly in time or space. Consider the Babyboom dataset we saw in Lecture 2. The birth times of the babies throughout the day are shown in Figure 1. If we divide up the day into 24 hour intervals and count the number of births in each hour we can plot the counts as a histogram in Figure 2. How does this compare to the histo...

2 θ + respectively. Shanker [2] has discussed its mathematical and statistical properties including its shape, moments, skewness, kurtosis, hazard rate function, mean residual life function, stochastic orderings, mean deviations, distribution of order statistics, Bonferroni and Lorenz curves, Renyi entropy measure, stress-strength reliability, amongst others along with the estimation of paramet...

The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies, and motivate the need for multi...

This paper presents the analysis of a continuous review perishable inventory system wherein the life time of each item follows an exponential distribution. The operating policy is (s,S) policy where the ordered items are received after a random time which follows exponential distribution. Primary arrival follows Poisson distribution and they may turnout to be posit...

*Correspondence: [email protected] 1Department of Mathematics and Statistics, Georgetown University, 306 St. Mary’s Hall, Washington, DC, 20057, USA Full list of author information is available at the end of the article Abstract The Poisson, geometric and Bernoulli distributions are special cases of a flexible count distribution, namely the Conway-Maxwell-Poisson (CMP) distribution – a two-pa...

Mixed Poisson distributions are widely used in various disciplines including actuarial applications. The family of mixed Poisson distributions contains several members according to the choice of the mixing distribution for the parameter of the Poisson distribution. Very few of them have been studied in depth, mainly because of algebraic intractability. In this paper we will describe an EM type ...