Unit Burr-III distribution with application

Modi, Kanak; Gill, Vinod

doi:10.1080/09720510.2019.1646503

Cited by 18 publications

(12 citation statements)

References 7 publications

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“…e other contributing term to the derivative is (− e λ E i [− λ]) which assumes negative values and increases with higher values of λ. us, derivative (19) can be a positive or negative number or zero depending on the values of GEUD parameters involved. Table 3 in Appendix, for the comprehension of entropic trends, presents Shannon entropies of several GEU distributions as well as the derivatives at selected positions of λ when xed θ is given di erent values.…”

Section: Theoremmentioning

confidence: 99%

“…(i) Beta distribution (BD) (ii) Unit-Weibull distribution (UWD) [18] (iii) Unit-Burr III distribution (UBIIID) [19] (iv) Unit-Gompertz distribution (UGomD) [20] e parameters of each model are estimated by the MLE method, and for the assessment of their adequacy, we use Akaike Information Criterion AIC � − 2L + 2k and Bayesian Information Criterion BIC � − 2L + k log(n).…”

Section: Applicationsmentioning

confidence: 99%

See 1 more Smart Citation

An Analysis of Generalized Exponential Uniform Distribution

Haq

Memon

Chand

2022

Mathematical Problems in Engineering

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A two-parameter distribution under “Generalized Exponential Uniform Distribution (GEUD)” is proposed in this paper by using the idea of Alzaatreh et al. (2013). We investigate its various properties including its characterization, hazard rate, mean residual life, and Shannon entropy. The constraints on its parameters generate three disjoint subfamilies with regard to their distribution characteristics that exhibit more adaptability when compared with other existing models in the literature for fitting real-life datasets with observations limited in the range (0,1). For the estimation of its parameters, we consider and compare the maximum likelihood, distance minimizing Anderson–Darling, and Cramer–von Mises approaches through simulation studies. To display the importance of this model, we provide its important applications. The GEUD model relative to other models is more suitable in describing certain real datasets.

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Section: Theoremmentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

An Analysis of Generalized Exponential Uniform Distribution

Haq

Memon

Chand

2022

Mathematical Problems in Engineering

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“…us, the researchers proposed and studied various unit distributions. Among the most useful unit distributions, there are the Johnson distribution [2], Topp-Leone distribution [3], unit-gamma distribution [4], Kumaraswamy distribution [5], log-Lindley distribution [6], unit-logistic distribution [7], unit-Birnbaum-Saunders distribution [8], log-xgamma distribution [9], unit-Lindley distribution [10], unit-Gompertz distribution [11], unit-inverse Gaussian distribution [12], unit-Bur III distribution [13], log-weighted exponential distribution [14], unit-Weibull distribution [15], unit-Modified Burr III distribution [16], unit-Rayleigh distribution [17], Frechet power function distribution [18], and unit-Burr XIII distribution [19].…”

Section: Introductionmentioning

confidence: 99%

A Unit Probabilistic Model for Proportion and Asymmetric Data: Properties and Estimation Techniques with Application to Model Data from SC16 and P3 Algorithms

Eliwa

Haq

Al‐Bossly

et al. 2022

Mathematical Problems in Engineering

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In this study, a new one-parameter Log-XLindley distribution is proposed to analyze the proportion data. Some of its statistical and reliability properties, including moments with associated measures, hazard rate function, reversed hazard rate, stress strength reliability, and mean residual life function, are investigated in closed forms which help the researchers for modeling data in a small CPU time. It is found that the density function of the introduced distribution can be used as a statistical tool to model asymmetric data. Moreover, the failure rate function can be utilized to model different types of failures, including increasing, bathtub, and J-shaped. The model parameter is estimated using various estimation approaches to get the best estimator to help us in modeling the real data in a good way with high accuracy. A Monte-Carlo simulation study for different sample sizes is performed to assess the performance of the estimations based on some statistical criteria. Finally, two distinctive data sets from SC16 and P3 algorithms, “estimating unit capacity factors,” are analyzed to illustrate the flexibility of the new model.

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“…Besides conventional beta and Kumaraswamy distributions, another type of unit distributions are proposed by using variable transformation (e.g. [4,15,16]). Recently, a Unit-Generalized Rayleigh (UGR) distribution is proposed by [11].…”

Section: Introductionmentioning

confidence: 99%

Inference and prediction of progressive Type-II censored data from Unit-Generalized Rayleigh distribution

Wang

Zuo

2022

Hacettepe Journal of Mathematics and Statistics

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In this paper, inference and prediction problems are studied under progressively Type-II censored data. When the latent lifetime follows the Unit-Generalized Rayleigh distribution, maximum likelihood estimators of the unknown parameters are established, and corresponding existence and uniqueness are also provided. Besides, the approximate confidence intervals are constructed based on asymptotic approximation theory. For comparison, another alternative generalized point and interval estimates are constructed based on proposed pivotal quantities. Further, point and interval predictions for the censored samples are established by using conventional classical and generalized inferential approaches. Finally, extensive simulation studies are carried out to investigate the performance of different methods, and one real-life example is presented to illustrate the applicability of the obtained results.

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Unit Burr-III distribution with application

Cited by 18 publications

References 7 publications

An Analysis of Generalized Exponential Uniform Distribution

An Analysis of Generalized Exponential Uniform Distribution

A Unit Probabilistic Model for Proportion and Asymmetric Data: Properties and Estimation Techniques with Application to Model Data from SC16 and P3 Algorithms

Inference and prediction of progressive Type-II censored data from Unit-Generalized Rayleigh distribution

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