Characterizations of the Beta Kumaraswamy Exponential Distribution

Al-Saiary, Zakeia A.; Bakoban, R. A.; Al-zahrani, Areej A.

doi:10.3390/math8010023

Cited by 8 publications

(8 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Skewness describes about the consistency of the data. Here we have used Bowley's coefficient of skewness by Al-saiary et al [1] based on quantiles as…”

Section: Skewness and Kurtosismentioning

confidence: 99%

See 1 more Smart Citation

Extended Kumaraswamy Exponential Distribution with Application to COVID-19 Data set

Chaudhary,

Sah Telee,

Kumar

2023

J. Nep. Math. Soc.

View full text Add to dashboard Cite

There are many probability models describing the time related events data. In this study, the exponential distribution is modified by adding one more parameter to get more flexible probability model called Extended Kumaraswamy Exponential (EKwE) distribution using the New Kw-G family (NKwG) of distributions. We have studied some of the statistical characteristics of the model, such as its reliability function, hazard rate function, and quantile function. For testing the applicability of the model, a real data set based on COVID-19 data is taken. The Cramer-von Mises (CVM) approach, Least Square Estimation (LSE), and Maximum Likelihood Estimation (MLE) are used to estimate the model’s parameters. Validity of the model is checked by using P-P plot and Q-Q plot. Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC) and Hannan-Quinn Information Criterion (HQIC) are also used for model comparison. Goodness of fit of the proposed model is tested using Kolmogrov-Smirnov (KS), Cramer-Von Mises (CVM) and Anderson-Darling (An) test statistics along with respective p-values. All the analysis of the study is performed by using R programming.

show abstract

“…Skewness describes about the consistency of the data. Here we have used Bowley's coefficient of skewness by Al-saiary et al [1] based on quantiles as…”

Section: Skewness and Kurtosismentioning

confidence: 99%

“…Coefficient of Octiles Kurtosis by Moors [14] and Al-saiary et al [1] can be calculated using relation…”

Section: Skewness and Kurtosismentioning

confidence: 99%

Extended Kumaraswamy Exponential Distribution with Application to COVID-19 Data set

Chaudhary,

Sah Telee,

Kumar

2023

J. Nep. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Then by using Eqs. ( 22)- (25), we obtain the posterior mean for GIED with Jeffrey's prior as E½a x j ffi n=T:…”

Section: Jeffrey's Priormentioning

confidence: 99%

“…The fitting performance is evaluated by Kolmogorov-Smirnov (K-S) statistic and some information criteria. A model is the best if it has the lowest Akaike information criteria (AIC), loglikelihood (LL), Bayesian information criterion (BIC), consistent Akaike information criterion (CAIC), and Hannan-Quinn information criterion (HQIC) [25]. The formulas of these criteria are…”

Section: Applications To Real Datamentioning

confidence: 99%

Bayesian Approximation Techniques for the Generalized Inverted Exponential Distribution

Bakoban¹,

Aldahlan²

2022

Intelligent Automation &Amp; Soft Computing

View full text Add to dashboard Cite

In this article, Bayesian techniques are adopted to estimate the shape parameter of the generalized inverted exponential distribution (GIED) in the case of complete samples. Normal approximation, Lindley's approximation, and Tierney and Kadane's approximation are used for deriving Bayesian estimators. Different informative priors are considered, such as Jeffrey's prior, Quasi prior, modified Jeffrey's prior, and the extension of Jeffrey's prior. Non-informative priors are also used, including Gamma prior, Pareto prior, and inverse Levy prior. The Bayesian estimators are derived under the quadratic loss function. Monte Carlo simulations are carried out to make a comparison among estimators based on the mean square error of the estimates. All estimators using normal, Lindley's, and Tierney and Kadane's approximation techniques perform consistently since the MSE decreases as the sample size increases. For large samples, estimators based on non-informative priors using normal approximation are usually better than the ones using Lindley's approximation. Two real data sets in reliability and medicine are applling to the GIED distribution to assess its flexibility. By comparing the estimation results with other generalized models, we prove that estimating this model using Bayesian approximation techniques gives good results for investigating estimation problems. The models compared in this research are generalized inverse Weibull distribution (GIWD), inverse Weibull distribution (IWD), and inverse exponential distribution (IED).

show abstract

“…Ref. [16] studied the beta KE model and some of its statistical properties, such as: moments, quantile function, median, mode, skewness, kurtosis, mean deviation and order statistics; also, they used medical data to show the importance of their model. Ref.…”

Section: Introductionmentioning

confidence: 99%

A New Extension of the Kumaraswamy Exponential Model with Modeling of Food Chain Data

Eldessouky

Hassan

Elgarhy

et al. 2023

Axioms

View full text Add to dashboard Cite

Statistical models are useful in explaining and forecasting real-world occurrences. Various extended distributions have been widely employed for modeling data in a variety of fields throughout the last few decades. In this article we introduce a new extension of the Kumaraswamy exponential (KE) model called the Kavya–Manoharan KE (KMKE) distribution. Some statistical and computational features of the KMKE distribution including the quantile (QUA) function, moments (MOms), incomplete MOms (INMOms), conditional MOms (COMOms) and MOm generating functions are computed. Classical maximum likelihood and Bayesian estimation approaches are employed to estimate the parameters of the KMKE model. The simulation experiment examines the accuracy of the model parameters by employing Bayesian and maximum likelihood estimation methods. We utilize two real datasets related to food chain data in this work to demonstrate the importance and flexibility of the proposed model. The new KMKE proposed distribution is very flexible, more so than numerous well-known distributions.

show abstract

Characterizations of the Beta Kumaraswamy Exponential Distribution

Cited by 8 publications

References 23 publications

Extended Kumaraswamy Exponential Distribution with Application to COVID-19 Data set

Extended Kumaraswamy Exponential Distribution with Application to COVID-19 Data set

Bayesian Approximation Techniques for the Generalized Inverted Exponential Distribution

A New Extension of the Kumaraswamy Exponential Model with Modeling of Food Chain Data

Contact Info

Product

Resources

About