The beta compound Rayleigh distribution : Properties and applications

Abstract

In this paper, we introduce a new four parameter continuous model, called the beta compound Rayleigh (BCR) distribution that extends the compound Rayleigh distribution. Basic properties of the proposed distribution such as; mean, variance, coefficient of variation, raw and incomplete moments, skewness, kurtosis, moment and probability generating functions, reliability analysis, Lorenz, Bonferroni and Zenga curves, Rényi of entropy, order statistics and record statistics are investigated. We obtain the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the usefulness of the new model.

The type I half-logistic Burr X distribution: theory and practice

“…The numerical values of these measures for the TIHL BX and the other competing distributions of the first data are provided in Table 3 and for the second data set in Table 4. The competing distributions includes the beta BurrX (BBX) by [17], beta compound Rayleigh (BCR) [25], transmuted generalized Rayleigh (TGR) [15], Weibull Rayleigh (WR) [16], exponentiated generalized inverse Weibull (EGIW) [9], generalized half-logistic Poisson (GHLP) [20], half-logistic Poisson (HLP) [22], Kumaraswamy Exponentiated Inverse Rayleigh (KwEIR) [2], Transmuted Rayleigh (TR) [14], generalized BurrXII Poisson (GBXIIP) [18], type I half-logistic Frechet (TIHL-Fr) [6], complimentary exponentiated BurrXII Poisson (CEBXIIP) [21], Burr-XII (BXII) and Burr-X (BX) (or generalized Rayleigh (GR)) by [5] and Rayleigh (R) distributions.…”

“…The first data set consists of 63 observations of the strengths of 1.5 cm glass fibers obtained by workers at the UK National Physical Laboratory. [17,25,26].…”

“…If θ 1 2 , the hazard function is bathtub and for θ > 1 2 it has an increasing hazard function. There are several extensions and generalizations of the Burr X (BX) distributions (or generalized Rayleigh (GR)), for example, beta generalized Rayleigh (BGR) by [7], the exponentiated generalized Burr type X (EGBX) by [12], beta Burr X by [17], and beta compound Rayleigh by [25], among others.…”