Tan-G class of trigonometric distributions and its applications

Souza, Luciana Sandra Bastos de; Júnior, Wilson Rosa de O.; Brito, Cícero Carlos Ramos de; Chesneau, Christophe; Fernandes, Renan; Ferreira, Tiago A. E.

doi:10.4067/s0719-06462021000100001

Cited by 32 publications

(22 citation statements)

References 11 publications

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“…As indicated by its name, Souza et al [ 28 ] introduced a new method for extending the classical probability distributions, leading to greater flexibility in analyzing and modelling different data types. They looked at a parent distribution, which is an arbitrary continuous probability distribution with a cdf and a corresponding pdf.…”

Section: The Proposed Familymentioning

confidence: 99%

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Modelling the COVID‐19 Mortality Rate with a New Versatile Modification of the Log‐Logistic Distribution

Muse¹,

Tolba

Fayad

et al. 2021

Computational Intelligence and Neuroscience

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The goal of this paper is to develop an optimal statistical model to analyze COVID-19 data in order to model and analyze the COVID-19 mortality rates in Somalia. Combining the log-logistic distribution and the tangent function yields the flexible extension log-logistic tangent (LLT) distribution, a new two-parameter distribution. This new distribution has a number of excellent statistical and mathematical properties, including a simple failure rate function, reliability function, and cumulative distribution function. Maximum likelihood estimation (MLE) is used to estimate the unknown parameters of the proposed distribution. A numerical and visual result of the Monte Carlo simulation is obtained to evaluate the use of the MLE method. In addition, the LLT model is compared to the well-known two-parameter, three-parameter, and four-parameter competitors. Gompertz, log-logistic, kappa, exponentiated log-logistic, Marshall–Olkin log-logistic, Kumaraswamy log-logistic, and beta log-logistic are among the competing models. Different goodness-of-fit measures are used to determine whether the LLT distribution is more useful than the competing models in COVID-19 data of mortality rate analysis.

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Section: The Proposed Familymentioning

confidence: 99%

“…Recently, Souza et al [ 28 ] proposed and studied the Burr-XII tangent distribution which serves as a potential lifetime model. Ampadu [ 29 ] introduced and studied the Weibull tangent distribution with applications to health science data.…”

Section: The Proposed Familymentioning

confidence: 99%

Modelling the COVID‐19 Mortality Rate with a New Versatile Modification of the Log‐Logistic Distribution

Muse¹,

Tolba

Fayad

et al. 2021

Computational Intelligence and Neuroscience

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show abstract

“…In the framework of the S-ML model, a simulation study is carried out to study the performance of θ given as Equation (10) in terms of their bias (bias) and mean squared error (MSE). The simulated procedure can be described as follows:…”

Section: Simulation Studymentioning

confidence: 99%

“…It enhances the parental power Lomax distribution on several functional aspects. Among the trigonometric families of distributions, a few of them, including the C-S family by [7], SKum-G family by [8], STL-G family by [9], and T-G family by [10], were influenced by these efforts.…”

Section: Introductionmentioning

confidence: 99%

The Sine Modified Lindley Distribution

Tomy¹,

Veena²,

Chesneau

2021

MCA

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The paper contributes majorly in the development of a flexible trigonometric extension of the well-known modified Lindley distribution. More precisely, we use features from the sine generalized family of distributions to create an original one-parameter survival distribution, called the sine modified Lindley distribution. As the main motivational fact, it provides an attractive alternative to the Lindley and modified Lindley distributions; it may be better able to model lifetime phenomena presenting data of leptokurtic nature. In the first part of the paper, we introduce it conceptually and discuss its key characteristics, such as functional, reliability, and moment analysis. Then, an applied study is conducted. The usefulness, applicability, and agility of the sine modified Lindley distribution are illustrated through a detailed study using simulation. Two real data sets from the engineering and climate sectors are analyzed. As a result, the sine modified Lindley model is proven to have a superior match to important models, such as the Lindley, modified Lindley, sine exponential, and sine Lindley models, based on goodness-of-fit criteria of importance.

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“…Furthermore, they might lead to additional new problems that allow more exploration of computational techniques, simulation, and algorithms. The following are some statistical distributions, or families of distributions, based on trigonometric functions: Fisher (F) distribution by [1], Von Mises (VM) distribution by [2], beta-trigonometric (BT) distribution by [3], circular Cauchy (CC) distribution by [4], sine square (SS) distribution by [5], sine-generated (SG) family by [6,7], cosine-generated (CSG) family by [8], new cosine-sine-generated (NCSG) family by [9], transformed sine-generated (TSG) family by [10], new sine-generated (NSG) family by [11], tan-generated (TG) family by [12], polyno-expo-trigonometric (PET) family by [13], sin Topp-Leone-generated (STLG) family by [14], sine extended odd Fréchetgenerated (SEOFG) family by [15], new exponential with trigonometric function (NET) distribution by [16], weighted cosine exponential distribution by [17], arc-sine distribution, and raised cosine distribution, among others. In particular, the SG, CSG, NSG, TG, STLG, and SEOFG families benefit from the oscillating nature of trigonometric functions to enrich the modeling capabilities of any chosen baseline distribution.…”

Section: Introductionmentioning

confidence: 99%

A New Extended Cosine—G Distributions for Lifetime Studies

et al. 2021

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In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution and probability density functions, moments, moments of residual life, reliability parameter, and order statistics. Three special members of the family are proposed and discussed, namely, the extended cosine Weibull, extended cosine power, and extended cosine generalized half-logistic distributions. Maximum likelihood, least-square, percentile, and Bayes methods are considered for parameter estimation. Simulation studies are used to assess these methods and show their satisfactory performance. The stress–strength reliability underlying the extended cosine Weibull distribution is discussed. In particular, the stress–strength reliability parameter is estimated via a Bayes method using gamma prior under the square error loss, absolute error loss, maximum a posteriori, general entropy loss, and linear exponential loss functions. In the end, three real applications of the findings are provided for illustration; one of them concerns stress–strength data analyzed by the extended cosine Weibull distribution.

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Tan-G class of trigonometric distributions and its applications

Cited by 32 publications

References 11 publications

Modelling the COVID‐19 Mortality Rate with a New Versatile Modification of the Log‐Logistic Distribution

Modelling the COVID‐19 Mortality Rate with a New Versatile Modification of the Log‐Logistic Distribution

The Sine Modified Lindley Distribution

A New Extended Cosine—G Distributions for Lifetime Studies

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