Sine-Exponential Distribution: Its Mathematical Properties and Application to Real Dataset

Isa, Alhaji Modu; Bashiru, Sule Omeiza; Ali, Alhaji Buhari; Adepoju, Akeem Ajibola; Itopa, Ibrahim Ismaila

doi:10.56919/usci.1122.017

Cited by 5 publications

(3 citation statements)

References 7 publications

(7 reference statements)

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“…In this paper, we focused on Sine G family proposed by Kumar et al (2015) to develop a new probability distribution called the Sine-Lomax Distribution. Some compounding of baseline distribution with the Sine G family proposed by Kumar et al (2015) includeSine Power Lomax by Nagarjuna et al (2021), Sine Modified Lindley distribution by Tomy et al (2021),Sine-Exponential distribution by Isa et al (2022a), and Sine Burr XII by Isa et al (2022b) among others.…”

Section: Lomax Distributionmentioning

confidence: 99%

Sine-Lomax Distribution: Properties and Applications to Real Data Sets

Mustapha,

Isa,

Sule

et al. 2023

FJS

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In this study, a novel distribution called the two-parameter Sine Lomax distribution was introduced. The distribution was developed by combining the Sine generalized family of distributions with the Lomax distribution. Various statistical properties of this new distribution were investigated, including the survival function, hazard function, quantile function, rth moment, entropy, moment generating function, and order statistics. The probability density function (PDF) plot indicated that the distribution is skewed to the right. Additionally, the hazard plot of the Sine Lomax distribution showed both monotonic increase and monotonic decrease. To estimate the parameters of the newly proposed distribution, the maximum likelihood approach was employed. A simulation study was conducted to evaluate the consistency of the estimators. The simulation results indicated that the estimators are consistent, as the bias and mean square error decrease with increasing sample sizes. The performance of the Sine Lomax distribution was compared to other extensions of Lomax distributions and the baseline distribution which is the Lomax distribution using various evaluation criteria, including the Akaike Information Criterion (AIC), Consistent Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC), and Hannan-Quinn Information Criterion (HQIC). The proposed distribution demonstrated the lowest scores among the competing models, indicating its potential for accurately modeling real-world data sets. Based on the results, the proposed Sine Lomax distribution is recommended as a superior alternative to the competing models for modeling certain real-world data sets.

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Section: Lomax Distributionmentioning

confidence: 99%

Sine-Lomax Distribution: Properties and Applications to Real Data Sets

Mustapha,

Isa,

Sule

et al. 2023

FJS

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“…[10] introduced the alpha-sine-G family of distributions, which extends the sine transformation family by adding a parameter. [11] developed the Sine Exponential Distribution, which combines the Sine-G generator with the Exponential Distribution. [12] introduces the Tan-G class, a general class of trigonometric distributions based on the tangent function, and focuses on the Tan-BXII distribution.…”

Section: Introductionmentioning

confidence: 99%

Marshall-Olkin Cosine Topp-Leone Family of Distributions with Application to Real-life Datasets

Osi,

Doguwa,

Yahaya

et al. 2024

Preprint

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The Marshall-Olkin (MO) family of distributions is a flexible framework that is adept at modeling complex dependence structures and tail behaviors in a variety of real-life datasets. This paper introduces a new member of the MO family called the Marshall-Olkin Cosine Topp-Leone G family. We derive several mathematical properties of this family, including the moment, moment generating function, Renyi's entropy, and the distribution of order statistics. We also provide some special cases of this class. To estimate the model parameters, we use the method of maximum likelihood. We explore the performance of this method through simulation studies, which show that biases and root-mean-square errors decrease as the sample size increases. To demonstrate the usefulness of our model, we apply it to two real-world datasets. Our findings show that, in comparison with existing distributions, our model provides the best fit for these data.

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“…Furthermore, Shrahili et al [36] introduced the Sine inverted exponential distribution, and Tomy and Chesneau [41] defined the Sine modified Lindley distribution using the Sine-G family of distribution. Additionally, Chaudhary et al [6] presented the arctan generalized exponential distribution with a flexible hazard rate, and Isa et al [22] defined the Sine exponential distribution and investigated its properties. Its CDF and PDF respectively are as follows…”

mentioning

confidence: 99%

Arc-Tangent Exponential Distribution With Applications to Weather and Chemical Data Under Classical and Bayesian Approach

Sapkota,

Alsahangiti,

Kumar

et al. 2023

IEEE Access

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This paper introduces the Arctan exponential distribution, a novel two-parameter trigonometric distribution. Various statistical properties of the distribution are examined, including hazard rate functions, cumulative hazard rate functions, mean deviation, reliability function, moments, conditional moments, incomplete moments, quantile function, entropy, Lorenz and Bonferroni curves, order statistics, and symmetry measures such as skewness and kurtosis. The parameters of the proposed distribution are estimated using the maximum likelihood estimation method, and a simulation study is conducted to assess its performance. Two real datasets are utilized to demonstrate the significance of the proposed distribution, showing that it performs comparably or better than well-known distributions. Furthermore, the suggested Arctan exponential distribution is employed within the Bayesian framework. The model's parameters are estimated and predicted using posterior samples generated through the application of the Markov Chain Monte Carlo (MCMC) technique. The application of the suggested model involves employing the Stan software in conjunction with the Hamiltonian Monte Carlo (HMC) algorithm and its adaptive variant known as the No-U-turn sampler (NUTS). A real dataset is utilized to showcase the methodology, and both numerical and graphical Bayesian analyses are performed, employing weakly informative priors. A posterior predictive check is also conducted to evaluate the model's predictability. The tools and methods employed in this study adhere to the Bayesian approach and are implemented using the R statistical programming language.INDEX TERMS Arctan distribution, Posterior distribution, Gamma prior, Credible interval, Lorenz curve I. INTRODUCTIONStatistical distributions play a pivotal role in the field of probability theory and statistics, providing a mathematical framework to describe the behavior of random variables and the likelihood of various outcomes in a given dataset or phenomenon. These distributions are fundamental building blocks for various statistical analyses and inference tech-niques. By characterizing the patterns and variability of data, statistical distributions enable researchers and analysts to make informed decisions, draw meaningful conclusions, and quantify uncertainties in their findings. Each distribution possesses unique properties and parameters that capture specific data characteristics, such as central tendency, spread, and shape. The selection of an appropriate distribution de-

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Sine-Exponential Distribution: Its Mathematical Properties and Application to Real Dataset

Cited by 5 publications

References 7 publications

Sine-Lomax Distribution: Properties and Applications to Real Data Sets

Sine-Lomax Distribution: Properties and Applications to Real Data Sets

Marshall-Olkin Cosine Topp-Leone Family of Distributions with Application to Real-life Datasets

Arc-Tangent Exponential Distribution With Applications to Weather and Chemical Data Under Classical and Bayesian Approach

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