A New Statistical Model Based on the Novel Generalized Odd Beta Prime Family of Continuous Probability Distributions with Applications to Cancer Disease Data Sets

Abstract

Statistical modeling of lifetime data plays an essential role in a wide range of practical fields, such as health and engineering. There have been a lot of studies done to develop statistical models that can better describe health data than traditional models. For the first time, we pioneer a novel family of continuous probability distributions called the generalized odd beta prime generalized (GOBP-G) family of distributions. The cumulative distribution and probability density functions of the new family are presented. A new generalization of the Weibull distribution called "generalized odd beta prime-Weibull" (GOBPW) is proposed using the pioneered GOBP-G family. The mixture representations of the new distribution are defined and derived. Some formal statistical properties of the GOBPW distribution, such as the moments, moment generating function, incomplete moments, information generating function, entropies, stress-strength function, quantile function, and order statistics, are derived. The estimation of the parameters of the proposed distribution is evaluated using the maximum likelihood estimation approach. Different cancer disease data sets, such as the bladder, head and neck, acute bone, and blood cancers, are used to illustrate the applicability and usefulness of the new model and were compared using several statistical accuracy measures with that of well-established extended Weibull distributions, which are the beta modified Weibull distribution, Kumaraswamy modified Weibull distribution, gamma generalized modified Weibull distribution, gamma log-logistic Weibull distribution, and beta log-logistic Weibull distribution. The results show that the proposed model gives better results than the competitive models. This study could guide the relevant stakeholders in choosing a suitable statistical model for the health data instead of relying on traditional models to enhance decision-making.

Log-Kumaraswamy distribution: its features and applications

“…Putting ( 27) into (26) gives the information generating function of the log-Kumaraswamy distribution as…”

“…Moreover, several new families of probability distributions have been introduced for modeling data in hydrology, medical science, engineering, insurance, and finance based on the Kumaraswamy distribution method, for instance, Kumaraswamy Weibull [12], Kumaraswamy generalized gamma [13], Kumaraswamy inverse Weibull [14], Kumaraswamy modified inverse Weibull [14], F-Weibull [15], Kumaraswamy Gumbel [16], Kumaraswamy log-logistic [17], Kumaraswamy exponentiated Pareto [18], Kumaraswamy modified Weibull [19], Kumaraswamy generalized Lomax [20], Kumaraswamy [21], Kumaraswamy half-Cauchy [22], Kumaraswamy generalized Rayleigh [23], Kumaraswamy skew-normal [24], Kumaraswamy inverse Weibull Poisson [25], odd beta prime-logistic distribution [26], Kumaraswamy Marshall-Olkin Fréchet [27], Kumaraswamy inverse flexible Weibull [28], Maxwell-exponential distribution [29], Kumaraswamy Laplace [30], extensions of the Gompertz and inverse Gaussian, Kumaraswamy Gompertz and Kumaraswamy inverse Gaussian distributions under the Kumaraswamy family of distributions [31], Kumaraswamy skew-t distribution [32], Kumaraswamy transmuted Pareto distribution [33], Kumaraswamy Marshall-Olkin log-logistic distribution [34], Kumaraswamy exponentiated Fréchet distribution [35], Kumaraswamy log-logistic Weibull distribution [36], Kumaraswamy alpha power inverted exponential distribution [37], Kumaraswamy Marshall-Olkin exponential distribution [38], odd beta prime Fréchet distribution [39], Kumaraswamy Inverted Topp-Leone distribution [40], log-Topp-Leone distribution [41], Kumaraswamy Harris generalized Kumaraswamy distribution [42], and generalized transmuted-Kumaraswamy distribution [43]. As studied in [44], Kumaraswamy's cumulative distribution function (cdf) with shape parameters α, β > 0 is given as…”

Families of Extended Exponentiated Generalized Distributions and Applications of Medical Data Using Burr III Extended Exponentiated Weibull Distribution

“…This section provide applicability of the new developed BIIIEEWD by empirical datasets consisting cancer diseases, such as blood, neck and head, acute bone, and bladder cancers. The efficiency of BIIIEEWD is checked and compared with other competing models, including generalized odd beta prime Weibull (GOBPW) (Suleiman et al, 2022) [17], gamma log-logistic Weibull (GmLLW) (Foya et al, 2017) [18], gamma generalized modified Weibull (GmGMoW) (Oluyede et al, 2015) [19], beta modified Weibull (BMoW) (Silva et al, 2010) [20], Kumaraswamy modified Weibull (KmMoW) (Cordeiro et al 2012) [21], and beta log-logistic Weibull (BeLLW) (Makubate et al, 2018) [22].…”

The Odd Beta Prime Inverted Kumaraswamy Distribution with Application to COVID-19 Mortality Rate in Italy

“…In the past few years, there has been significant interest in extending conventional distribution models to better capture real-life data by employing a generalized class of distributions. These include the extended Gumbel-Weibull distribution from [23], the generalized odd beta prime family of distributions from [24], the new extended Topp-Leone exponential distribution from [25], the log-Topp-Leone distribution from [26], the Marshall-Olkin extended Gumbel type-II distribution from [27], the McDonald generalized power Weibull distribution from [28], the exponentiated odd Lomax exponential distribution from [29], the Maxwell-Weibull distribution from [30], the Maxwell-exponential distribution from [31], the odd-F-Weibull distribution from [32], and many others. Recently, reference [33] developed a new family of distribution referred to as the odd beta prime-G (OBP-G) family.…”