Theory and Applications of the Transmuted Continuous Bernoulli Distribution

Chesneau, Christophe; Opone, Festus C.; Ubaka, Ngozi O.

doi:10.34198/ejms.10222.385407

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…It is, therefore, important to remark that the APTL distribution is the first-lifetime distribution belonging to the alpha power transformed family of distributions that has its support on a unit interval [0, 1]. Other non-nested generalized lifetime distributions with support [0, 1] are found in the works of [21]- [27]. It is hoped that the APTL distribution will be a strong competitor unit distribution in fitting data sets defined on a unit interval.…”

Section: Introductionmentioning

confidence: 99%

The Alpha Power Topp-Leone Distribution: Properties, Simulations and Applications

Ehiwario¹,

Igabari²,

Ezimadu³

2023

JAMP

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This paper presents an extended lifetime probability distribution based on the alpha power transformation. We refer to the proposed distribution as "the Alpha Power Topp-Leone (APTL) distribution". Mathematical properties of the APTL distribution such as the density and cumulative distribution functions, survival and hazard rate functions, quantile function, median, moments and its relative measures, probability weighted moment, moment generating function, Renyi entropy, and the distribution of order statistics were derived. The method of maximum likelihood estimation was employed to estimate the unknown parameters of the APTL distribution. Finally, we used two real data sets obtained from the literature to illustrate the applicability of the APTL distribution in real-life data fitting.

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Section: Introductionmentioning

confidence: 99%

The Alpha Power Topp-Leone Distribution: Properties, Simulations and Applications

Ehiwario¹,

Igabari²,

Ezimadu³

2023

JAMP

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A Bounded Lifetime Distribution Specified by a Trigonometric Function: Properties, Regression Model, and Applications

Ogumeyo,

Opone,

Abubakari

et al. 2024

International Journal of Mathematics and Mathematical Sciences

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Trigonometric functions have gained considerable attention in recent studies for developing new lifetime distributions. This is due to their parsimonious framework, mathematical tractability, and flexibility of the newly developed distributions. In this paper, the Sine‐generated family is used to create a new bounded lifetime distribution, known as Sine‐Marshall–Olkin Topp–Leone distribution, for modeling data defined on the unit interval. Some statistical properties of the new bounded distribution, including quantile function, ordinary moments, incomplete moments, moment‐generating functions, inequality measures, Rényi entropy, and probability weighted moments are derived. Seven methods of parameter estimation, including maximum likelihood, ordinary least squares, weighted least squares, moment product spacing, Anderson–Darling, and Cramér–von Mises estimators are used to estimate the parameters of the new distribution. The behavior of the estimators obtained from the estimation methods are investigated using Monte Carlo simulation studies. The results show that the estimation methods are asymptotically efficient and consistent. The flexibility of the new bounded distribution is examined via data fitting using two proportional datasets. The results of the fittings show that the new bounded distribution performs significantly better than the competing bounded lifetime distributions. Finally, Sine‐Marshall–Olkin Topp–Leone regression model is presented as an alternative to the beta and Kumaraswamy regression models.

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Study of the inverse continuous Bernoulli distribution

Opone,

Christophe CHESNEAU

2024

Malaya J. Mat.

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The continuous Bernoulli distribution, a one-parameter probability distribution defined over the interval [0, 1], has recently garnered increased attention in the realm of applied statistics. Numerous studies have underscored both its merits and limitations, alongside proposing extended variants. In this article, we introduce an innovative modification of the continuous Bernoulli distribution through an inverse transformation, thereby introducing the inverse continuous Bernoulli distribution. The main characteristic of this distribution lies in its transposition of the continuous distribution’s properties onto the interval \( [1, +\infty)\), without necessitating any additional parameters. The initial section of this article elucidates the mathematical properties of this novel inverse distribution, encompassing essential probability functions and quantiles. Inference for the associated model is carried out via the widely employed maximum likelihood estimation method. To evaluate the efficacy of the estimated model, a comprehensive simulation study is conducted. Subsequently, the model’s performance is assessed in a practical context, using data sets from a diverse array of sources. Notably, our findings demonstrate its superior performance in comparison to a broad spectrum of analogous models defined over the support interval \( [1, +\infty)\), even surpassing the established Pareto model.

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Theory and Applications of the Transmuted Continuous Bernoulli Distribution

Cited by 3 publications

References 13 publications

The Alpha Power Topp-Leone Distribution: Properties, Simulations and Applications

The Alpha Power Topp-Leone Distribution: Properties, Simulations and Applications

A Bounded Lifetime Distribution Specified by a Trigonometric Function: Properties, Regression Model, and Applications

Study of the inverse continuous Bernoulli distribution

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