Unit Modified Burr-III Distribution: Estimation, Characterizations and Validation Test

Haq, Muhammad Ahsan ul; Hashmi, Sharqa; Aidi, Khaoula; Ramos, Pedro Luiz; Louzada, Francisco

doi:10.1007/s40745-020-00298-6

Cited by 24 publications

(10 citation statements)

References 20 publications

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“…X = e −Y Unit Weibull [12] Unit Gompertz [13] Unit Rayleigh [14] Unit gamma/Gompertz [15] Unit Gamma [16] The log-xgamma [17] Unit generalized half-normal [18] Unit Chen [19] Unit Nadarajah and Haghighi [20] Unit Inverse Guassian [21] Unit Burr-XII [22] Unit Power Logarithmic [23] X = Y ∕1 + Y One parameter unit Lindley [24] Modified unit Burr-III [25] X = 1∕1 + Y One parameter new unit Lindley [26] Y = 1 − (1 + X) − 1…”

Section: Transformation Referenced Unit-bounded Interval Distributionsmentioning

confidence: 99%

Study of a bounded interval perks distribution with quantile regression analysis

Al‐Essa,

Shafiq,

Ozonur

et al. 2024

Statistical Analysis

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In this article, a novel bounded interval model called the unit‐Perks model is developed by suitably transforming the positive random variable of the Perks distribution. Numerous statistical features of the bounded interval Perks model are being explored based on the expansion of the density function. Eight distinct estimation approaches are being used to estimate the parameters of the unit‐Perks model. A throughout simulation analysis is also included to evaluate the precision of the resulting estimators from eight estimating approaches. Two real bounded interval data sets are being utilized to investigate the practical applicability of the unit‐Perks model. A comparison is also made to determine which method of estimation works better for the given model. According to a comparison of eight different estimation approaches, the maximum likelihood estimation approach outperformed than the other seven estimating approaches. The unit‐perks model is then used to introduce the quantile regression model named as quantile unit‐Perks distribution. Application to real data set for the quantile unit‐Perks distribution is also performed. The quantile residuals are used for the residual analysis of the fitted regression model. On the basis of mathematical, computational, and pictorial evidences, it is concluded that the presented model exhibited greater modeling capabilities.

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Section: Transformation Referenced Unit-bounded Interval Distributionsmentioning

confidence: 99%

Study of a bounded interval perks distribution with quantile regression analysis

Al‐Essa,

Shafiq,

Ozonur

et al. 2024

Statistical Analysis

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“…Some of these distributions includes the Topp-Leone distribution [4] . The unit-gamma distribution [5] is one of the few unit interval distributions we are aware of, as well as the following more recent ones: Log-Lindley distribution [6] , the two-parameter unit logistic distribution [7] , the two-parameter unit-Birnbaum–Saunders distribution [8] , unit-Gompertz [9] , unit-inverse Gaussian distribution [10] , unit-Rayleigh distribution [11] , the unit-Weibull distribution [12] , unit modified Burr-III distribution [13] and log-weighted exponential(WE) distribution [14] , transmuted unit Rayleigh quantile regression model [15] , unit generalized half-normal quantile regression model [16] , unit generalized log Burr XII distribution [17] and unit folded normal distribution [18] .…”

Section: Introductionmentioning

confidence: 99%

Unit upper truncated Weibull distribution with extension to 0 and 1 inflated model – Theory and applications

Okorie,

Afuecheta,

Bakouch

2023

Heliyon

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“…Several probability distributions have been developed in this area for dealing with restricted datasets in various domains using the previous transformation. Among the most notable distributions are: unit gamma (Grassia [3] and Tadikamalla [4]), unit logistic (Tadikamalla and Johnson [5] and Menezes et al [6]), unit Birnbaum-Saunders (Mazucheli et al [7]), unit Weibull (Mazucheli et al [8,9]), unit inverse Gaussian (Ghitany et al [10]), unit Gompertz (Mazucheli et al [11]), unit Lindley (Mazucheli et al [12]), unit generalized half-normal (Korkmaz [13]), unit modified Burr-III (Haq et al [14]), unit Burr-XII (UBXII) (Korkmaz and Chesneau [15]), unit gamma/Gompertz (Bantan et al [16]), unit log-logistic (Ribeiro-Reis [17]), and unit generalized log Burr XII (UGLBXII) (Bhatti et al [18]). In addition to the preceding transformations, Cancho et al [19] and Rodrigues et al [20] developed a broad strategy based on the cumulative distribution function (CDF)-quantile function (QF).…”

Section: Motivation and Introductionmentioning

confidence: 99%

Bayesian and Non-Bayesian Inference for Unit-Exponentiated Half-Logistic Distribution with Data Analysis

et al. 2022

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Unit distributions are typically used in probability theory and statistics to illustrate useful quantities with values between zero and one. In this paper, we investigated an appropriate transformation to propose the unit-exponentiated half-logistic distribution (UEHLD), which is also beneficial for modelling data on the unit interval. This distribution’s mathematical features are supplied, including moments, probability-weighted moments, incomplete moments, various entropy measures, and stress–strength reliability. Using well-known estimation techniques such as the maximum likelihood, maximum product of spacing, and Bayesian inference, the estimators of the parameters relevant to the proposed distribution were determined. A comprehensive simulation analysis is provided to examine the performance of parameter estimation approaches on finite samples. The proposed distribution was realistically applied to data on economic growth and data on the tensile strength of polyester fibers to provide an explanation. Furthermore, the analysis of COVID-19 data from Britain as a medical statistical dataset is provided. The experimental results demonstrate that the suggested UEHLD yields a better comparison with some new unit distributions, as well as other unbounded distributions.

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Unit Modified Burr-III Distribution: Estimation, Characterizations and Validation Test

Cited by 24 publications

References 20 publications

Study of a bounded interval perks distribution with quantile regression analysis

Study of a bounded interval perks distribution with quantile regression analysis

Unit upper truncated Weibull distribution with extension to 0 and 1 inflated model – Theory and applications

Bayesian and Non-Bayesian Inference for Unit-Exponentiated Half-Logistic Distribution with Data Analysis

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