The Gamma Odd Burr III-G Family of Distributions: Model, Properties and Applications

Abstract

A new family of distributions called Ristic-Balakhrishnan Odd Burr III-G (RBOB III-G) distribution is proposed. We obtain some mathematical and statistical properties of this distribution such as hazard and reverse hazardfunctions, quantile function, moments and generating functions, conditional moments, Rényi entropy, order statistics, stochastic ordering and probability weighted moments. The model parameters are estimated using maximum likelihood estimation technique. Finally, the usefulness of this family of distributions is demonstrated via simulation experiments.

A New Nadarajah-Haghighi Generalization with Five Different Shapes for the Hazard Function

“…The derivation of generalized distributions by adding parameters to an existing model is an instrumental technique in the statistical literature (Oluyede & Liyanage, 2023). These generalized models have been proposed to obtain flexible models, which can accommodate different configurations of skewness and non-monotonic shapes for the hrf (Marinho et al, 2018).…”

“…These generalized models have been proposed to obtain flexible models, which can accommodate different configurations of skewness and non-monotonic shapes for the hrf (Marinho et al, 2018). We can cite Silva et al (2019) and Peter et al (2021) as some recent advances in the distribution theory.…”

Half Logistic Inverted Nadarajah–Haghighi Distribution under Ranked Set Sampling with Applications

“…They are ideally suited for the prediction and forecasting of real-world issue modeling. There are several ways for generalizing distributions, including: beta-G [1]; generalized Kumaraswamy-G [2]; Weibull odd Burr III-G [3]; Gompertz-G [4]; a new power Topp-Leone-G [5]; exponentiated Kumaraswamy-G [6]; type I half logistic Weibull-G [7]; type I half logistic Burr X-G [8]; the transmuted Burr X-G in [9]; odd power Lindley-G [10]; gamma Kumaraswamy-G [11]; new extended cosine-G in [12]; extended-gamma-G [13]; odd Chen-G [14]; Kumaraswamy type I half logistic-G [15]; log-logistic-G [16]; gamma-G [17]; Kumaraswamy Poisson-G [18]; Kumaraswamy Kumaraswamy-G [19]; additive odd-G [20]; beta generalized Marshall-Olkin Kumaraswamy-G [21]; extended alpha power transformed family of distributions [22]; odd Burr X-G [23]; the Weibull−G in [24]; type II half logistic-G [25]; sec-G [26]; generalized odd linear exponential-G [27]; Stacy-G [28]; odd Perks-G [29]; sine Topp-Leone-G [30]; Kumaraswamy generalized Marshall-Olkin-G [31]; arcsine-exponentiated-X family-G [32]; odd exponentiated half logistic-G [33]; Kumaraswamy Marshall-Olkin-G [34]; and sineexponentiated Weibull−H [35], among others. Recently, ref.…”

The Gamma Odd Weibull Generalized-G Family of Distributions: Properties and Applications

“…Over the years, several new and very useful families of distributions have been developed and new generalized distributions obtained by adding one or more parameters to existing distributions in the statistical literature including the Transform-transformer (T-X) by Alzaghal et al (2013), Weibull-G by Bourguignon et al (2014), beta-G by Eugene et al (2002), McDonald-G (Mc-G) by Alexander et al (2012) and Lomax generator by Cordeiro et al (2014), Kumaraswamy odd log-logistic family by Alizadeh, Emadi, Doostparast, Cordeiro, Ortega & Pescim (2015), Kumaraswamy Marshall-Olkin family by Alizadeh, Tahir, Cordeiro, Mansoor, Zubair & Hamedani (2015). Peter et al (2021) developed and studied the gamma odd Burr III family of distributions. Cordeiro et al (2013) introduced a class of distributions called the exponentiated generalized (EG) class of distributions.…”