Half Cauchy-Modified Exponential Distribution: Properties and Applications

Chaudhary, Arun Kumar; Kumar, Vijay

doi:10.3126/njmathsci.v3i1.44125

Cited by 6 publications

(5 citation statements)

References 9 publications

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“…A variety of probability models utilizing the Cauchy family of distributions are presented in the literature. These models include the Half-Cauchy exponential extension distribution (Telee & Kumar, 2022) [30] , the Arc tan generalized exponential distribution (Chaudhary et al, 2021) [7] , the generalized Cauchy family of distributions (Alzaatreh et al, 2016), the Pareto ArcTan (PAT) distribution (Gómez-Déniz and Calderín-Ojeda, 2015) [14] , and the Half-Cauchy modified exponential distribution (Chaudhary et al, 2022).…”

Section:  mentioning

confidence: 99%

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:  mentioning

confidence: 99%

Cauchy modified generalized exponential distribution: Estimation and Applications

Chaudhary,

Telee,

Kumar

2024

Int. J. Stat. Appl. Math.

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“…Chaudhary and Kumar [7] introduced the logistic NHE distribution using the extension of exponential distribution by Nadarajah and Haghighi [16]. Chaudhary and Kumar [8] have also developed new model called half-Cauchy modified exponential distribution using half-Cauchy family of distribution by Ristić and Balakrishnan [19]. There are many modified distributions.…”

Section: Introductionmentioning

confidence: 99%

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

Chaudhary,

Sah Telee,

Kumar

2023

J. Nep. Math. Soc.

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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.

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“…Cordeiro et al (2017) [6] has developed the family of distribution using half-Cauchy distribution as generalized odd half-Cauchy family of distribution. By utilizing the family of half-Cauchy distributions as the baseline model, the half Cauchy modified exponential distribution has suggested by (Chaudhary & Kumar, 2022) [3] . In order to improve the inverse Gompertz distribution's fit to the real data, we suggest the half-Cauchy inverse Gompertz distribution, a more flexible distribution that only requires one extra parameter.…”

Section: Introductionmentioning

confidence: 99%

Half-cauchy inverse Gompertz distribution: Theory and applications

Chaudhary¹,

Yadav²,

Kumar³

2022

Int. J. Stat. Appl. Math.

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In this paper, we have introduced a new distribution named half Cauchy inverse Gompertz distribution using the family of half-Cauchy distribution as base line distribution. Some crucial statistical properties of the new distribution are deliberated and analyzed. To evaluate the model parameters of the new model, we have applied the three commonly used estimation methods namely LSE, CVM and MLE. For the evaluation of flexibility and adaptability of the new model we have consider a real dataset and compared the goodness-of-fit attained by proposed distribution with some competing distribution. It is found that the suggested model is good fitted a real data set and more flexible as compared to a few other models.

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Half Cauchy-Modified Exponential Distribution: Properties and Applications

Cited by 6 publications

References 9 publications

Cauchy modified generalized exponential distribution: Estimation and Applications

Cauchy modified generalized exponential distribution: Estimation and Applications

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

Half-cauchy inverse Gompertz distribution: Theory and applications

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