A new beta generated Kumaraswamy Marshall-Olkin-G family of distributions with applications

Abstract

Unification of the recently introduced Kumaraswamy Marshall-Olkin-G and Beta Marshall-Olkin-G family of distributions is proposed. A number of important statistical and mathematical properties of the family is investigated. A distribution belonging to the proposed family is shown to perform better than the corresponding distribution from the Kumaraswamy Marshall-Olkin-G and Beta Marshall-Olkin-G family of distributions by considering data fitting with three real life data sets.

Characterizations of the Beta Kumaraswamy Exponential Distribution

“…The hazard function is the instant rate of failure at a given time t, while the reliability function is the probability of the non-failure occurring before time t. The reliability function of the BKw-E distribution is given by: (14) and the corresponding hazard function of the BKw-E distribution takes the form Figure 2 shows the reliability curves for different values of the parameters for the BKw-E distribution, while Figure 3 shows that the hazard function of the BKw-E distribution increases for different values of (a, b, λ, l, m). The BKw-E distribution shows good statistical behavior based on these two functions.…”

“…Furthermore, they discussed the Monte Carlo simulation, and applications with real data were provided. Reference [14] proposed the beta-generated Kumaraswamy-G family. They obtained some of its properties; the order statistics, probability weighted moments, moment-generating function, and Rényi entropy were also derived.…”

Beta Kumaraswamy Burr Type X Distribution and Its Properties

“…Our second motivation, lies within the wide usage of Kum-G family define in equation (7) and the baseline distribution known as the BX define in equation (11) together with the property of beta-G family define in equation (5) and (6) above due the relative flexibility and capability in modeling agriculture, engineering and medical datasets in respect to the model suitability at different tractable or complex situations. However, we were motivated to introduced this new model called Beta Kumaraswamy Burr Type X (Beta Kum-BX) with six parameters θ = ν, κ, ϕ, ψ, ϑ and τ by confounding equation (9) and (11) and also equation (10) and (12) by the methods of beta-G generator proposed by [8] and thereby Burr Type X as the baseline distribution which we obtain the probability density function PDF given as:…”

“…A new model was introduced called Beta Kumaraswamy Burr type X (Beta Kum-BX) with six parameters (ν, κ, ϑ, ψ, ϑ, τ ) that extends the Kum-G family, and Burr type X distributions by the family of Beta Kum-G family which was proposed by [8]. We obtain the distributional properties like: PDF, CDF and shapes of hazard function and their expansions.…”

Truncated Weibull-G More Flexible and More Reliable than Beta-G Distribution

“…Recently, several new distributions have been introduced following the proposed work by Eugene et al (2002), including the betaGumble and beta-exponential distributions by Nadarajah andKots (2004,2006), respectively, beta-Weibull distribution by Lee, Famoye and Olumolade (2007), beta-generalized exponential distribution by Barreto-Souza, Santos and Cordeiro (2010), beta-modified Weibull distribution by Silva, Ortega and Cordeiro (2010), beta-Weibull-geometric distribution by Cordeiro, Silva and Ortega (2013), beta-generalized gamma distribution by , beta-lindley distribution by MirMostafaee, Mahdizadeh and Nadarajah (2015) and beta-generalized Marshall-Olkin-G family by Handique and Chakraborty (2016).…”