A new distribution having three parameters called Exponentiated Inverse Chen distribution is proposed in this study. Important statistical properties like Survival function, hazard rate function, skewness and kurtosis etc are studied. Some methods of estimation Least Square, Maximum likelihood and Cramer-Von Mises methods are used using R programming software. A data set is discussed and Validity of the model is tested by analyzing P-P and Q-Q plots. Different information criteria such as Akanke’s information criterion, Bayesian information criterion, Corrected Akanke’s information criterion, and Hannan – Quinn information criterion are applied for model comparisons. For testing the goodness of fit of the proposed model, Kolmogrov-Smirnov, Anderson darling and Cramer –Von Mises statistics are used. The proposed model called Exponentiated Inverse Chen distribution is more applicable as compared to some existing probability model. It is found that MLEs are better with respect to LSE and CVM. PDF curve of model has shown that it can have various shapes like increasing as well as decreasing, monotonically increasing, constant as well as inverted bathtub shaped based hazard function is seen. Applicability and suitability of model is evaluated. For this, we have considered a real-life dataset. We found distribution that EIC is much flexible.

Background: New family of distributions has important functions in generalization of distributions by modifying some existing distributions for getting more flexible irrespective to applied and practical view point. The Inverse Exponentiated Odd Lomax Exponential Distribution (IEOLE) having four parameters is suggested. Proposed model is based on T-X family of distribution which is the extended form of beta-generated distribution. Based on the LSE, MLE, and CVM methods, the parameters of the proposed distribution are estimated. Different model validation criteria and model comparisons are done by considering other existing models. Materials and methods: IEOLE is compound distribution derived by using theoretical concept of Odd Lomax Exponential distribution and T-X family of distribution. The parameters of the proposed distribution are estimated through the least square, Cramer–Von Mises and maximum likelihood methods. The applicability of the proposed model is evaluated using R programming on two real-life time data sets. Results: The statistical properties and different characteristics like the hazard rate function, the cumulative distribution function, quantile function, skewness, and kurtosis of the proposed model are discussed. Box plots, TTT plot, density fits etc. shows that the proposed model fits better to considered two real data sets. Different model validation criteria such as AIC, BIC, and CAIC are obtained and compared with some existing well-known probability distributions. Conclusion: This study presents new probability model called Inverse Exponentiated Odd Lomax Exponential distribution. The density curves of the model show that it is unimodal having right skewed. The suggested model has proven to be versatile for modeling real-world data due to its increasing-decreasing, right-skewed form. Also, the hazard rate function (HRF) graph is decreasing, decreasing-increasing or inverted bathtub shaped according to the value of the model constants. Different validation criteria show that the suggested model fits data well and the goodness-of-fit shows that proposed model has lesser test statistic value and higher p- value with respect to some existing models.

In this article, we have proposed three parameters distribution using lindley family of distribution and Generalized inverted Exponential distribution called Lindley Generalized Inverted Exponential Distribution: Model and Applications(LGIE). The statistical properties as well as different characteristics like the hazard rate function (HRF), the probability density function (PDF), the cumulative distribution function (CDF), quantile function , skewness, and kurtosis of the proposed distribution are discussed. The parameters of the proposed distribution are estimated by using the maximum likelihood estimation (MLE), least-square estimation (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R programming software. To assess the application of the proposed distribution, a real lifetime data set is analyzed and performed the goodness-of-fit.

This paper is based on new extension of the exponential distribution named “Exponentiated Exponential Poisson Inverse (IEEP) distribution”. The distribution is based on lifetime issues containing three parameters. Likelihood method is used to estimate the parameters of the distribution. Explicit expressions for reliability/survival function, the hazard rate function, reversed hazard rate, the quantile function and mode are introduced. Maximum Likelihood estimates as well as asymptotic confidence interval are obtained using theory of the Maximum likelihood. For illustration and application, a real data set is analyzed and compared with three other model of literature. Model fitted here is better compared to other models for data considered. All the graphical and computation analysis is performed using R programming.

In this article, we have introduced a new probability distribution called Modified Exponentiated Inverted Exponential (MEIE) Distribution. The introduced model is right tailed increasing- decreasing hazard rate function. We have discussed some statistical properties like probability density function, cumulative distribution function, survival function and hazard rate function etc. Model parameters are estimated via Maximum Likelihood, Least Squares, and Cramer-Von Mises estimation techniques. To check the applicability a real data set is taken and the model validation is checked using different information criteria as well as using some graphical techniques. For model comparison we have considered some published probability model.