In this article we study some properties of a new family of distributions, namely Exponentiated Exponential distribution, discussed in Gupta, Gupta, and Gupta (1998). The Exponentiated Exponential family has two parameters (scale and shape) similar to a Weibull or a gamma family. It is observed that many properties of this new family are quite similar to those of a Weibull or a gamma family, th...

Two SEIR models with quarantine and isolation are considered, in which the latent and infectious periods are assumed to have an exponential and gamma distribution, respectively. Previous studies have suggested (based on numerical observations) that a gamma distribution model (GDM) tends to predict a larger epidemic peak value and shorter duration than an exponential distribution model (EDM). By...

A general program was written which simulates radioactive labeling of RNA in viva. The program was used to determine the effect that different -distributions of half-lives would have on the composite decay curve observed in a pulse-chase experiment. Four biologically relevant points emerge: 1) The published, experimentally determined composite decay curves for eukaryotic mRNA are not compatible...

We consider the problem of forecasting multi-class job flow times in a resource-sharing environment. We assume the deviation of flow times in each class from the class nominal value follows an exponential distribution with its parameter following a gamma distribution. A large simulation experiment is conducted to assess and compare the performance of the Bayes and empirical Bayes forecasting me...

The analyzing and modeling real lifetime data are crucial in many applied sciences including medicine, engineering, insurance and finance, amongst others. The two important one parameter lifetime distributions namely exponential and Lindley [2] are popular for modeling lifetime data from biomedical science and engineering. Recently, Shanker et al. [3] have conducted a comparative and critical s...

The negative binomial distribution has become increasingly popular as a more flexible alternative to Poisson distribution, especially when it is questionable whether the strict requirements for Poisson distribution could be satisfied. But negative binomial distribution is better for overdispersed count data that are not necessarily heavy-tailed, for heavy tailed count data the traditional stati...

Rameshwar D. Gupta was the speaker of a seminar titled “Generalized Exponential Distributions”. Gupta received his PhD degree in statistics from Dalhousie University in 1973. He worked in the University of the West Indies, University of Saskatchewan. He joined the University of New Brunswick in 1980. He has received the Merit Award at the University of New Brunswick at Saint John four times. Pr...

Definition 1.1 Let N(0, 1) denote the one dimensional normal distribution. This distribution has density n(x) = e−x 2/2/ √ 2π. LetNd(0, 1) denote the d-dimensional Gaussian distribution, induced by picking each coordinate independently from the standard normal distribution N(0, 1). Let Exp(λ) denote the exponential distribution, with parameter λ. The density function of the exponential distribu...

It can be seen that a mixture of an exponential distribution and a gamma distribution with increasing failure rate for the right choice of parameters can yield a distribution with a bathtub-shaped failure rate. In this paper we consider a continuous mixture of exponentials and a continuous mixture of gammas with increasing failure rates and show that the resulting mixture has a bathtub-shaped f...