Abstract
A new class of distributions called the beta linear failure rate power series (BLFRPS) distributions is introduced and discussed. This class of distributions contains new and existing sub-classes of distributions including the beta exponential power series (BEPS) distribution, beta Rayleigh power series (BRPS) distribution, generalized linear failure rate power series (GLFRPS) distribution, generalized Rayleigh power series (GRPS) distribution, generalized exponential power series (GEPS) distribution, Rayleigh power series (RPS) distributions, exponential power series (EPS) distributions, and linear failure rate power series (LFRPS) distribution of Mahmoudi and Jafari (2014). The special cases of the BLFRPS distribution include the beta linear failure rate Poisson (BLFRP) distribution, beta linear failure rate geometric (BLFRG) distribution of Oluyede, Elbatal and Huang (2014), beta linear failure rate binomial (BLFRB) distribution, and beta linear failure rate logarithmic (BLFRL) distribution. The BLFRL distribution is also discussed in details as a special case of the BLFRPS class of distributions. Its structural properties including moments, conditional moments, deviations, Lorenz and Bonferroni curves and entropy are derived and presented. Maximum likelihood estimation method is used for parameters estimation. Maximum likelihood estimation technique is used for parameter estimation followed by a Monte Carlo simulation study. Application of the model to a real dataset is presented.
Highlights
A NEW GENERALIZED CLASS OF LINEAR FAILURE RATE POWER SERIES DISTRIBUTIONBoikanyo Makubate[1], Masego Otlaadisa[1], Broderick O
In recent years, many techniques for the modeling lifetime data have been introduced.Beta-G family of distributions of Eugene et al (2002) is one of the techniques used in modeling lifetime issues
Taking the G(y; ψ) to be the linear failure rate power series (LFRPS) distribution, that is the marginal cdf of Y, we obtain the cdf of the new class of distributions called the beta linear failure rate power series (BLFRPS) as FBLFRPS(y; a, b, α, β, θ)
Summary
Boikanyo Makubate[1], Masego Otlaadisa[1], Broderick O. Fagbamigbe[1], Alphonso Amey[1]. *2Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460,USA
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