A New Marshall-Olkin Extended Family of Distributions with Bounded Support

Ubaka

2022

EJMS

Modern applied statistics naturally give rise to the continuous Bernoulli distribution (data fitting, deep learning, computer vision, etc). On the mathematical side, it can be viewed as a one-parameter distribution corresponding to a special exponential distribution restricted to the unit interval. As a matter of fact, manageable extensions of this distribution have great potential in the same fields. In this study, we motivate a transmuted version of the continuous Bernoulli distribution with the goal of analyzing proportional data sets. The feature of the created transmuted continuous Bernoulli distribution is an additional parameter that realizes a linear tradeoff between the min and max of two continuous random variables with the continuous Bernoulli distribution. The standard study process is respected: we derive some mathematical properties of the proposed distribution and adopt the maximum likelihood estimation technique in estimating the unknown parameters involved. A Monte Carlo simulation exercise was conducted to examine and confirm the asymptotic behavior of the obtained estimates. In order to show the applicability of the proposed distribution, three proportional data sets are analyzed and the results obtained are compared with competitive distributions. Empirical findings reveal that the transmuted continuous Bernoulli distribution promises more flexibility in fitting proportional data sets than its competitors.

Section: Transmuted Schemementioning

confidence: 99%

Theory and Applications of the Transmuted Continuous Bernoulli Distribution

Chesneau

Ubaka

2022

EJMS

“…Some significant properties of the measure given in ( 19) is reported in Opone and Iwerumor [13] as;…”

Section: The Renyi Entropy Of the Kug Distributionmentioning

confidence: 99%

The Kumaraswamy Unit-Gompertz Distribution and its Application to Lifetime Datasets

Akata

Osagiede

2022

EJMS

This paper presents a new generalized bounded distribution called the Kumaraswamy unit-Gompertz (KUG) distribution. Some of the Mathematical properties which include; the density function, cumulative distribution function, survival and hazard rate functions, quantile, mode, median, moment, moment generating function, Renyi entropy and distribution of order statistics are derived. We employ the maximum likelihood estimation method to estimate the unknown parameters of the proposed KUG distribution. A Monte Carlo simulation study is carried out to investigate the performance of the maximum likelihood estimates of the unknown parameters of the proposed distribution. Two real datasets are used to illustrate the applicability of the proposed KUG distribution in lifetime data analysis.

“…Several generalizations of the distribution have been introduced to address the aforementioned drawback. These generalizations are found in the works of [1][2][3][4][5]9,10]. In this paper, we introduce a new generalization of the Topp-Leone distribution which serves as an alternative distribution among the Topp-Leone generated family of Diamond O. Tuoyo, Festus C. Opone and N. Ekhosuehi http://www.earthlinepublishers.com 382 distributions.…”

Section: Introductionmentioning

confidence: 99%

The Topp-Leone Weibull Distribution: Its Properties and Application

Tuoyo

Ekhosuehi

2021

EJMS

This paper presents a new generalization of the Topp-Leone distribution called the Topp-Leone Weibull Distribution (TLWD). Some of the mathematical properties of the proposed distribution are derived, and the maximum likelihood estimation method is adopted in estimating the parameters of the proposed distribution. An application of the proposed distribution alongside with some well-known distributions belonging to the Topp-Leone generated family of distributions, to a real lifetime data set reveals that the proposed distribution exhibits more flexibility in modeling lifetime data based on some comparison criteria such as maximized log-likelihood, Akaike Information Criterion [AIC=2k-2 log⁡(L) ], Kolmogorov-Smirnov test statistic (K-S) and Anderson Darling test statistic (A*) and Crammer-Von Mises test statistic (W*).