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

Chaudhary, Arun Kumar; Sah Telee, Lal Babu; Kumar, Vijay

doi:10.3126/jnms.v6i1.57657

Cited by 2 publications

(2 citation statements)

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“…We have chosen a few well-known distributions for comparison in order to show the CMGE distribution's goodness of fit. These are Modified Weibull (MW) (Lai et al, 2003) [20] , Odd Lomax Exponential (OLE) distribution (Ogunsanya et al, 2019), Generalized Exponential (GE) distribution (Gupta & Kundu, 1999a) [16] , Extended Kumaraswamy Exponential (EKwE) Distribution (Chaudhary et al, 2023) [10] . Table 3 presents the estimated parameter values and standard errors of the proposed models as well as those of competing models.…”

Section: ~61~mentioning

confidence: 99%

“…Several innovative probability models have been created through the ~57~ modification of exponential distributions found in literature. These distributions encompass a wide range of models, including the extended exponential distribution (Gomez et al, 2014) [15] , The modified exponential (ME) distribution (Rasekhi et al, 2017) [26] , the New Odd Generalized Exponential -Exponential Distribution (Kumar & Kumar, 2019) [19] , the Marshall-Olkin generalized exponential distribution (Ristic & Kundu, 2015), the beta generalized exponential distribution (Barreto-Souza et al, 2010) [6] , the Kumaraswamy-Generalized Exponentiated Exponential Distribution (Mohammed, 2014) [22] , Modified slashed generalized exponential distribution (Astorga et al, 2020) [5] , Weibull generalized exponential distribution (Almongy et al, 2021) [3] , Twoparameter modified weighted exponential distribution (Chesneau et al, 2022) [11] , Modified upside-down bathtub-shaped hazard function distribution (Chaudhary et al, 2023) [10] , and A New Four Parameter Extended Exponential Distribution (Hassan et al, 2022) [18] . These lifetime models might exhibit a hazard rate function (HRF) with a bathtub-shaped pattern.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Cauchy modified generalized exponential distribution: Estimation and Applications

Chaudhary,

Telee,

Kumar

2024

Int. J. Stat. Appl. Math.

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We present a unique probability model in this study called the Cauchy Modified Generalized Exponential Distribution. This model is formulated by combining the Cauchy family of distributions with the Modified Generalized Exponential Distribution as the baseline distribution. Our objective is to employ this model in the analysis of lifetime data. We've crafted formulas for various statistical functions, like skewness, kurtosis, survival function, quantile function, hazard rate function, distribution function, and probability density function. Additionally, we've integrated visual depictions of the probability density and hazard rate curves. We gathered a dataset that included notable earthquakes (magnitude 7.0 and higher) that the USGS had documented between 1990 and 2018. Our proposed model's effectiveness was evaluated by applying it to a global dataset covering significant earthquakes of the same magnitude range. The model parameters were estimated using maximum likelihood estimation. Several statistical measures were applied in order to confirm the validity of the model, including the Bayesian Information Criterion, Corrected Akaike's Information Criterion, the Hannan-Quinn Information Criterion, and Akaike's Information Criterion. Additionally, Q-Q and P-P plots were employed for validation. We used the Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises tests to evaluate how well our model fit the data. These tests were conducted to determine the suitability of our model for analyzing the provided earthquake data. Our empirical results indicate that, compared to alternative lifetime distributions, our suggested distribution not only exhibits a better fit but also provides increased flexibility for analyzing lifetime data. This study advances our understanding of earthquake patterns and contributes to the ongoing efforts in seismic risk assessment and mitigation strategies. All numerical calculations were performed using the R programming language.

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Section: ~61~mentioning

confidence: 99%