93 research outputs found
The Beta Maxwell Distribution
In this work we considered a general class of distributions gener- ated from the logit of the beta random variable. We looked at various works that have been done and discussed some of the results that were obtained. Special cases of this class include the beta-normal distribution, the beta-exponential distribution, the beta-Gumbell distribution, the beta-Weibull distribution, the beta-Pareto distribution and the beta-Rayleigh distribution. We looked at the probability distribution functions of each of these distributions and also look at some of their properties. Another special case of this family, a three-parameter beta-Maxwell distribution was dened and studied. Various properties of the distribution were also discussed. The method of maximum likelihood was proposed to estimate the parameters of the distribution
The Beta Generalized Exponential Distribution
We introduce the beta generalized exponential distribution that includes the
beta exponential and generalized exponential distributions as special cases. We
provide a comprehensive mathematical treatment of this distribution. We derive
the moment generating function and the th moment thus generalizing some
results in the literature. Expressions for the density, moment generating
function and th moment of the order statistics also are obtained. We discuss
estimation of the parameters by maximum likelihood and provide the information
matrix. We observe in one application to real data set that this model is quite
flexible and can be used quite effectively in analyzing positive data in place
of the beta exponential and generalized exponential distributions
A Generalization of the Exponential-Poisson Distribution
The two-parameter distribution known as exponential-Poisson (EP)
distribution, which has decreasing failure rate, was introduced by Kus (2007).
In this paper we generalize the EP distribution and show that the failure rate
of the new distribution can be decreasing or increasing. The failure rate can
also be upside-down bathtub shaped. A comprehensive mathematical treatment of
the new distribution is provided. We provide closed-form expressions for the
density, cumulative distribution, survival and failure rate functions; we also
obtain the density of the th order statistic. We derive the th raw moment
of the new distribution and also the moments of order statistics. Moreover, we
discuss estimation by maximum likelihood and obtain an expression for Fisher's
information matrix. Furthermore, expressions for the R\'enyi and Shannon
entropies are given and estimation of the stress-strength parameter is
discussed. Applications using two real data sets are presented
Statistical Properties of a Convoluted Beta-Weibull Distribution
A new class of distributions recently developed involves the logit of the beta distribution. Among this class of distributions are the beta-normal (Eugene et.al. (2002)); beta-Gumbel (Nadarajah and Kotz (2004)); beta-exponential (Nadarajah and Kotz (2006)); beta-Weibull (Famoye et al. (2005)); beta-Rayleigh (Akinsete and Lowe (2008)); beta-Laplace (Kozubowski and Nadarajah (2008)); and beta-Pareto (Akinsete et al. (2008)), among a few others. Many useful statistical properties arising from these distributions and their applications to real life data have been discussed in the literature. One approach by which a new statistical distribution is generated is by the transformation of random variables having known distribution function(s). The focus of this work is to investigate the statistical properties of the convoluted beta-Weibull distribution, defined and extensively studied by Famoye et al. (2005). That is, if X is a random variable having the beta-Weibull distribution with parameters a1, B1, c1, y1 i.e. X=BW(a1, B1, c1 and y1) and Y has a beta-Weibull distribution expressed as Y=BW(a2, B2, c2, y2) what then is the distribution of the convolution of X and Y. That is, the distribution of the random variable Z=X+Y. We obtain the probability density function (pdf) and the cumulative distribution function (cdf) of the convoluted distribution. Various statistical properties of this distribution are obtained, including, for example, moment, moment and characteristic generating functions, hazard function, and the entropy. We propose the method of Maximum Likelihood Estimation (MLE) for estimating the parameters of the distribution. The open-source software R is used extensively in implementing our results
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