Recently, several methods have been introduced to generate neoteric distributions with more exibility, like T-X, T-R [Y] and alpha power. The T-Inverse exponential [Y] neoteric family of distributons is proposed in this paper utilising the T-R [Y] method. A generalised inverse exponential (IE) distribution family has been established. The distribution family is generated using quantile functions of some dierent distributions. A number of general features in the T-IE [Y] family are examined, like mean deviation, mode, moments, quantile function, and entropies. A special model of the T-IE [Y] distribution family was one of those old distributions. Certain distribution examples are produced by the T-IE [Y] family. An applied case was presented which showed the importance of the neoteric family.
The Lomax distribution (or Pareto II) was first introduced by K. S. Lomax in 1954. It can be readily applied to a wide range of situations including applications in the analysis of the business failure life time data, economics, and actuarial science, income and wealth inequality, size of cities, engineering, lifetime, and reliability modeling. In his pioneering paper, Shannon 1948 defined the notion of entropy as a mathematical measure of information, which is sometimes called Shannon entropy in his honor. He laid the groundwork for a new branch of mathematics in which the notion of entropy plays a fundamental role over different areas of applications such as statistics, information theory, financial analysis, and data compression. [Ebrahimi and Pellerey 14] introduced the residual entropy function because the entropy shouldn't be applied to a system that has survived for some units of time, and therefore, the residual entropy is used to measure the ageing and characterize, classify and order lifetime distributions. In this paper, the estimation of the entropy and residual entropy of a two parameter Lomax distribution under a generalized Type-II hybrid censoring scheme are introduced. The maximum likelihood estimation for the entropy is provided and the Bayes estimation for the residual entropy is obtained. Simulation studies to assess the performance of the estimates with different sample sizes are described, finally conclusions are discussed.
An exponential-inverse-exponential {Weibull} regression failure model is introduced. Some of its properties like density function, survival function, and hazard function are derived. Maximum likelihood estimates of the parameters of the new model from censored data are obtained. To assess the local influence diagnostic(s) on the parameter estimates, the appropriate matrices are derived. Also, global influence and local influence are used to detect influential observations. Martingale and Deviance residuals are obtained and used to detect outliers and evaluate the model assumptions. A real data is analyzed under Log-Exponential-Inverse-Exponential {Weibull} regression model to show the usefulness of the model. A simulation study is performed to investigate the behavior of the estimates for different sample sizes and censoring percentages.
Statistical distributions play a major role in analyzing experimental data, and finding an appropriate one for the data at hand is not an easy task. Extending a known family of distribution to construct a new one is a long honored technique in this regard. The T-X[Y] methodology is utilized to construct a new distribution as described in this study. The T-inverse exponential family of distributions, which was previously introduced by the same authors, is used to examine the exponential-inverse exponential[Weibull] distribution (Exp-IE [Weibull]). Several fundamental properties are explored, including survival function, hazard function, quantile function, median, skewness, kurtosis, moments, Shannon's entropy, and order statistics. Our distribution exhibits a wide range of shapes with varying skewness and assume most possible forms of hazard rate function. The unknown parameters of the Exp-IE [Weibull] distribution are estimated via the maximum likelihood method for a complete and type II censored samples. We performed two applications on real data. The first one is vinyle chloride data, which is explained by [1] and the second is cancer patients data, which is explained by [2]. The significance of the Exp-IE [Weibull] model in relation to alternative distributions (Fréchet, Weibull-exponential, logistic-exponential, logistic modified Weibull, Weibull-Lomax [log-logistic] and inverse power logistic exponential) is demonstrated. When using the applied real data, the new distribution (Exp-IE[Weibull]) achieved better results for the AIC and BIC criterion compared to other listed distributions.
The Weibull-inverse exponential-loglogistic distribution which is abbreviated as (Weibull-IE-loglogistc) is a member of the neotric T- inverse exponential family introduced previously by the authors. Properties of this distribution such as (mode, quantile function, median, hazard function, survival function, moments, order statistics and Shannon’s entropy) are derived, and maximum likelihood estimates of its parameters are obtained. The usefulness of this neoteric distribution in analyzing data is illustrated. A simulation study is conducted to evaluate the performance of this distribution.
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