The beta Burr type X distribution properties with application

Abstract

We develop a new continuous distribution called the beta-Burr type X distribution that extends the Burr type X distribution. The properties provide a comprehensive mathematical treatment of this distribution. Further more, various structural properties of the new distribution are derived, that includes moment generating function and the rth moment thus generalizing some results in the literature. We also obtain expressions for the density, moment generating function and rth moment of the order statistics. We consider the maximum likelihood estimation to estimate the parameters. Additionally, the asymptotic confidence intervals for the parameters are derived from the Fisher information matrix. Finally, simulation study is carried at under varying sample size to assess the performance of this model. Illustration the real dataset indicates that this new distribution can serve as a good alternative model to model positive real data in many areas.

A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate

“…The data has previously been used by Smith and Naylor [17], Bourguinon et al [18], and Merovci et al [19] The performances of the GoLom distribution with the other competing distributions are shown in Table 4.…”

The beta-burr type v distribution: its properties and application to real life data

“…Where F(x)is the cumulative distribution function of the baseline distribution and f(x)is the probability density function of the baseline distribution Many researchers have used this technique to come up with many compound distributions which include: [1], [3], [4], [6], [8], [9], [12], [15], [16], [17], [18], [19], [20], [21], [23] and many others. The aim of this paper is to propose a new model called beta-Burr type V distribution.…”

“…So many researchers have established beta -G distribution; these include among others: Nadarajah and Gupta [20] defined the beta-Frechet distribution; Famoye, et al [5] defined the beta-Weibull; Nadaraja and Kotz [19] defined the betaexponential distribution; Kong et al [15] proposed the betagamma distribution. Fischer and Vaughan [12] introduced the beta-hyperbolic secant distribution; beta-Gumbel (BGU) distribution was introduced by Nadarajah and Kotz [18]; the beta-Pareto distribution was defined and studied by Akinsete et al [4]; the beta-Rayleigh distribution was proposed by Akinsete and Lowe [3]; beta-Burr XII by Paranaiba et al [21]; and very recently, Merovci et al [17] developed the beta-Burr type X distribution leaving the rest types of Burr distributions with little or no interest from researchers. This is the case with Burr type V distribution.…”

“…Ever since the introduction of the Burr distribution, it has somewhat been neglected as an option in the analysis of lifetime data. Even though there are researchers that indicate that this distribution possesses sufficient flexibility to make it a possible model for various types of data; for example, it was used to examine the strengths of 1.5 cm glass fibers [17], Paranaiba et al [21] studied cancer recurrence by using the real data set. Burr's type V distribution extension with two parameters is through the beta-G generator pioneered by Eugene et al [8].…”

Bivariate Beta Exponential Distributions

“…For more details, see, also, the beta-Pareto distribution by Akinsete, et al (2008), beta modified Weibull distribution by Silva et al(2010), beta generalized half-normal distribution by Pescim et al, (2010), And ,also, the beta Burr XII distribution by Paranaiba, et al, (2011), beta extended Weibull distribution by Cordeiro, et al(2012),beta exponentiated Weibull by Cordeiro et al(2013),beta-lindley distribution by Merovci and Sharma (2014), beta Burr type X distribution by Merovci et al,(2016). Eugene et al (2002) introduced the beta normal distribution by taking G(x) in (1) to be the cdf of the normal distribution.…”