On the Extended Generalized Inverted Kumaraswamy Distribution

Ramzan, Qasim; Qamar, Sadia; Amin, Muhammad; Alshanbari, Huda M.; Nazeer, Amna; Elhassanein, Ahmed

doi:10.1155/2022/1612959

Cited by 9 publications

(9 citation statements)

References 25 publications

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“…Proposition 8. Let Y ~UPWD ðα, β, λÞ for y ∈ ð0, 1Þ and α , β, λ > 0; then, its sth incomplete moments by using (18) and incomplete beta function β l ða, bÞ= l 0 x a−1 ð1 − xÞ b−1 dx are given by…”

Section: Sth Incomplete Momentmentioning

confidence: 99%

“…Proposition 9. Let Y ~UPWD ðα, β, λÞ for y ∈ ð0, 1Þ and α, β, λ > 0; then, its moment-generating function can be obtained by using (18) and replacing e ty = ∑ ∞ m=0 ðt m /m!Þy m is given by…”

Section: Sth Incomplete Momentmentioning

confidence: 99%

“…Again, we use the series expansions and mathematical maneuvering as we did to derive Equation (18), to arrive at…”

Section: Sth Incomplete Momentmentioning

confidence: 99%

“…The following points provide sufficient incentive to study the proposed model. We specify it as follows: (i) we employed a unique transformation to develop UPWD instead of employing traditional transformation found in literature to propose unit distributions which include Y = e −x , ð1 + xÞ −1 , or Y = ðxÞð1 + xÞ −1 , depending upon the functional identifiability of the baseline model; (ii) recent developments in distribution theory have shown a significant rise in the analysis of bivariate extensions of univariate models; for further information, we may refer the readers to see in [17][18][19][20]. So, we introduced and thoroughly explored a bivariate extension of a unit distribution, known as the bivariate unit-power Weibull distribution (BIUPWD for short) as far as no bivariate extension has been explored for the unit distributions in the literature.…”

Section: Introductionmentioning

confidence: 99%

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Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

Bantan

Shafiq

Tahir

et al. 2022

Journal of Function Spaces

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In this paper, a new distribution named as unit-power Weibull distribution (UPWD) defined on interval (0,1) is introduced using an appropriate transformation to the positive random variable of the Weibull distribution. This work offers quantile function, linear representation of the density, ordinary and incomplete moments, moment-generating function, probability-weighted moments, L -moments, TL-moments, Rényi entropy, and MLE estimation. Additionally, several actuarial measures are computed. The real data applications are carried out to underline the practical usefulness of the model. In addition, a bivariate extension for the univariate power Weibull distribution named as bivariate unit-power Weibull distribution (BIUPWD) is also configured. To elucidate the bivariate extension, simulation analysis and application using COVID-19-associated fatality rate data from Italy and Belgium to conform a BIUPW distribution with visual depictions are also presented.

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Section: Sth Incomplete Momentmentioning

confidence: 99%

Section: Sth Incomplete Momentmentioning

confidence: 99%

“…Again, we use the series expansions and mathematical maneuvering as we did to derive Equation (18), to arrive at…”

Section: Sth Incomplete Momentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

Bantan

Shafiq

Tahir

et al. 2022

Journal of Function Spaces

Self Cite

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show abstract

“…In the end, we are going to apply a variety of different optimality criteria to the censored samples that were created by the suggested model. For more reading, see Ramzan et al [ 43 ].…”

Section: Future Workmentioning

confidence: 99%

Novel Type I Half Logistic Burr-Weibull Distribution: Application to COVID-19 Data

Alshanbari

Odhah

Almetwally

et al. 2022

Computational and Mathematical Methods in Medicine

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In this work, we presented the type I half logistic Burr-Weibull distribution, which is a unique continuous distribution. It offers several superior benefits in fitting various sorts of data. Estimates of the model parameters based on classical and nonclassical approaches are offered. Also, the Bayesian estimates of the model parameters were examined. The Bayesian estimate method employs the Monte Carlo Markov chain approach for the posterior function since the posterior function came from an uncertain distribution. The use of Monte Carlo simulation is to assess the parameters. We established the superiority of the proposed distribution by utilising real COVID-19 data from varied countries such as Saudi Arabia and Italy to highlight the relevance and flexibility of the provided technique. We proved our superiority using both real data.

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A novel extended Kumaraswamy distribution and its application to COVID‐19 data

Suleiman,

Daud,

Ishaq

et al. 2024

Engineering Reports

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In the field of biomedical research, data characteristics often exhibit significant variability, challenging the applicability of classical probability distributions for biomedical data modeling. In this research, we introduce a novel four‐parameter distribution called the odd beta prime Kumaraswamy (OBPK) distribution, derived from the odd beta prime generalized family of distributions and the Kumaraswamy distribution. This distribution exhibits greater flexibility compared with the traditional Kumaraswamy distribution. Importantly, the OBPK distribution offers symmetrical, right‐skewed, left‐skewed, bathtub, N‐shaped, J‐shaped, and reversed J‐shaped densities, as well as varied hazard functions, including increasing, decreasing, bathtub, increasing‐decreasing, upside‐down bathtub, and N‐shaped forms. These curvature patterns make it particularly useful for modeling biomedical data. We derive some basic properties of the OBPK distribution. Parameters are estimated using the maximum likelihood approach, and the performance of various estimators is assessed via Monte Carlo simulations. Finally, four applications to real data on COVID‐19 mortality rates from different countries are evaluated to demonstrate the importance of the OBPK model over other extended versions of the Kumaraswamy models. The empirical findings suggest that the OBPK model outperforms other extended versions of the Kumaraswamy models in these applications.

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On the Extended Generalized Inverted Kumaraswamy Distribution

Abstract: In this work, we provide a new generated class of models, namely, the extended generalized inverted Kumaraswamy generated (EGIKw-G) family of distributions. Several structural properties (survival function sf , hazard rate function … Show more

Cited by 9 publications

References 25 publications

Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

Novel Type I Half Logistic Burr-Weibull Distribution: Application to COVID-19 Data

A novel extended Kumaraswamy distribution and its application to COVID‐19 data

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