This article sets out a simple formula for theoretical evaluation of the normal distribution function (F(z)) with greatest absolute error less than 5times;10^-8. The proposed formula is based on values of z agrave;454 (-acirc;21E,+acirc;21E) and is generated by applying polar integral,...

In this paper two new bivariate distributions are defined and studied. They are two-variate versions of the folded normal distribution (Leone et al. 1961) and the folded t distribution (Psarakis and Panaretos 1990).They both arise in the context of evaluating the predictive behaviour of two...

Control Charts are the main tools of Statistical Process Control. They are used for deciding whether a process is statistically stable or not. Much theory and many applications have been developed for the Gaussian (Normal) distribution in this area. However, in real data sets we usually face up...

Let X, Y be two discrete random variables with finite support and Xamp;#8805;Y. Suppose that the conditional distribution of Y given X can be factorized in a certain way. This paper provides a method of deriving the unique form of the marginal distribution of X (and hence the joint distribution of...

Two interesting results encountered in the literature concerning the Poisson and the negative binomial distributions are due to MORAN (1952) and PATIL amp; SESHADRI (1964), respectively. MORAN's result provided a fundamental property of the Poisson distribution. Roughly speaking, he has shown...

Compound Poisson distributions (CPD's) are frequently used as alternatives in studying situations where a simple Poisson model is found inadequate to describe. In this paper an attempt is made to identify compound Poisson distributions when it is known that the conditional distribution of two...

The binomial and multinomial distributions are, probably, the best known distributions because of their vast number of applications. The present paper examines some generalizations of these distributions with many practical applications. Properties of these generalizations are studied and models...

In this paper, distributions of items sampled inversely in clusters are derived. In particular, negative binomial type of distributions are obtained and their properties are studied. A logarithmic series, type of distribution is also defined as limiting form of the obtained generalized negative...

A model of Markov dependent trials is considered that leads to a generalization of the binomial distribution in the context of evaluating models of a time series by exploiting the sequential nature of model-based predictions. Adopting an evaluation method similar in nature to that suggested by...