The Inverse Epsilon Distribution as an Alternative to Inverse Exponential Distribution with a Survival Times Data Example

This paper is devoted to a new flexible two-parameter lower-truncated distribution, which is based on the inversion of the so-called epsilon distribution. It is called the inverse epsilon distribution. In some senses, it can be viewed as an alternative to the inverse exponential distribution, which has many applications in reliability theory and biology. Diverse properties of the new lower-truncated distribution are derived including relations with existing distributions, hazard and reliability functions, survival and reverse hazard rate functions, stochastic ordering, quantile function with related skewness and kurtosis measures, and moments. A demonstrative survival times data example is used to show the applicability of the new model.

A modified truncated distribution for modeling the heavy tail, engineering and environmental sciences data

Truncated models are imperative to efficiently analyze the finite data that we observe in almost all the real life situations. In this paper, a new truncated distribution having four parameters named Weibull-Truncated Exponential Distribution (W-TEXPD) is developed. The proposed model can be used as an alternative to the Exponential, standard Weibull and shifted Gamma-Weibull and three parameter Weibull distributions. The statistical characteristics including cumulative distribution function, hazard function, cumulative hazard function, central moments, skewness, kurtosis, percentile and entropy of the proposed model are derived. The maximum likelihood estimation method is employed to evaluate the unknown parameters of the W-TEXPD. A simulation study is also carried out to assess the performance of the model parameters. The proposed probability distribution is fitted on five data sets from different fields to demonstrate its vast application. A comparison of the proposed model with some extant models is given to justify the performance of the W-TEXPD.

Generalized fiducial inference on the mean of zero-inflated Poisson and Poisson hurdle models

Zero-inflated and hurdle models are widely applied to count data possessing excess zeros, where they can simultaneously model the process from how the zeros were generated and potentially help mitigate the effects of overdispersion relative to the assumed count distribution. Which model to use depends on how the zeros are generated: zero-inflated models add an additional probability mass on zero, while hurdle models are two-part models comprised of a degenerate distribution for the zeros and a zero-truncated distribution. Developing confidence intervals for such models is challenging since no closed-form function is available to calculate the mean. In this study, generalized fiducial inference is used to construct confidence intervals for the means of zero-inflated Poisson and Poisson hurdle models. The proposed methods are assessed by an intensive simulation study. An illustrative example demonstrates the inference methods.

The Truncated Power Lomax Distribution: Properties and Applications

A new truncated distribution, called the truncated power Lomax (TPL) distribution, is proposed. This is a truncated version of the power Lomax distribution. The TPL distribution has increasing and decreasing shapes of the hazard function. Some statistical properties, such as moments, survival, hazard, and quantile functions, are discussed. The maximum likelihood estimation (MLE) is constructed for estimating the unknown parameters of the TPL distribution. Moreover, the distribution has been fitted with real data sets to illustrate the usefulness of the proposed distribution. From the results of the example applications, the TPL distribution provides a consistently better fit than the other distributions, i.e., power Lomax and Lomax.