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.

Alpha Power Extended Inverse Weibull Poisson Distribution: Properties, Inference, and Applications to lifetime data

In this paper, a new four-parameter extended inverse Weibull distribution called Alpha power Extended Inverse Weibull Poisson distribution is introduced using the alpha power Poisson generator. This method adds two shape parameters to a baseline distribution thereby increasing its flexibility and applicability in modeling lifetime data. We study the structural properties of the new distribution such as the mean, variance, quantile function, median, ordinary and incomplete moments, reliability analysis, Lorenz and Bonferroni curves, Renyi entropy, mean waiting time, mean residual life, and order statistics. We use the method of maximum likelihood technique for estimating the model parameters of Alpha power extended inverse Weibull distribution and the corresponding confidence intervals are obtained. The simulation method is carried out to evaluate the performance of the maximum likelihood estimate in terms of their Absolute Bias and Mean Square Error using simulated data. Two lifetime data sets are presented to demonstrate the applicability of the new model and it is found that the new model has superior modeling power when compare to Inverse Weibull distribution, Alpha Power Poisson inverse exponential distribution, Alpha Power Extended Inverse Weibull distribution, and Alpha Power Extended Inverse Exponential distribution.

Inverse Akash distribution and its applications

A new one-parameter distribution named inverse Akash distribution, for modelling lifetime data, has been introduced. Important statistical properties of the proposed distribution such as the density function, hazard rate function, survival function, stochastic ordering, entropy measure, stress-strength reliability and the maximum likelihood estimation of the parameter of the distribution have been discussed. Two real data sets were employed in illustrating the usefulness of the new distribution. Comparatively, the inverse Akash distribution provided better fits to the data than each of the inverse exponential distribution and inverse Lindley distribution.

A New Extended Generalized Inverse Exponential Distribution: Properties and Applications

The quest by researchers in the area of distribution theory in proposing new models with greater flexibility has filled literature. On this note, we proposed a new distribution called the new extended generalized inverse exponential distribution with five positive parameters, which extends and generalizes the extended generalized inverse exponential distribution. We derive some mathematical properties of the proposed model including explicit expressions for the quantile function, moments, generating function, survival, hazard rate, reversed hazard rate, cumulative hazard rate function and odds functions. The method of maximum likelihood is used to estimate the parameters of the distribution. We illustrate its potentiality with applications to three real life data sets which show that the new extended generalized inverse exponential model provides greater flexibility and better fit than other competing models considered.

An Exponentiated Odd Lindley Inverse Exponential Distribution and its Application to Infant Mortality and HIV Transmission Rates in Nigeria

Recently, researchers have shown much interest in developing new continuous probability distributions by adding one or two parameter(s) to the some existing baseline distributions. This act has been beneficial to the field of statistical theory especially in modeling of real life situations. Also, the exponentiated family as used in developing new distributions is an efficient method proposed and studied for defining more flexible continuous probability distributions for modeling real life data. In this study, the method of exponentiation has been used to develop a new distribution called “Exponentiated odd Lindley inverse exponential distribution”. Some properties of the proposed distribution and estimation of its unknown parameters has been done using the method of maximum likelihood estimation and its application to real life datasets. The new model has been applied to infant mortality rate and mother-to-child HIV transmission rate. The results of these two applications reveal that the proposed model is a better model compared to the other fitted existing models by some selection information criteria.

Statistical Analysis of Mother-to-Child HIV Transmission Rate Using a Weibull-Exponential Inverse Exponential Distribution

Distribution functions, their properties and interrelationships play a significant role in modeling naturally occurring phenomena. Numerous standard distributions have been extensively used over the past decades for modeling data in several fields, however, generalizing these standard distributions has produced several compound distributions that are more flexible compared to the baseline distributions. Acquired immune deficiency syndrome is a disease caused by human immunodeficiency virus (HIV) that leads to a continuous decay of the human body immune system. Over the past few years, the rate of mother-to-child transmission of HIV has been on a non-decreasing trend in Nigeria and hence becoming a threat to the health of the nation. The Weibull generalized family of distributions has been efficient in developing new continuous probability distributions with additional two shape parameters. In this paper, a Weibull-based model has been proposed and it is called “a Weibull-Exponential Inverse Exponential distribution”. The properties, estimation of parameters and application of the new distribution are presented and discussed in this paper. Adequate application and investigation of the new model was done using a dataset on the rate of mother-to-child transmission of HIV and the result was compared with that of other competing models.

Modelling Mother-To-Child HIV Transmission Rate in Nigeria Using an Exponentiated Exponential Inverse Exponential Distribution

The act of adding extra parameters into existing distributions for increasing their flexibility or performance is a giant stride in the area of statistical theory and applications. Acquired immune deficiency syndrome (AIDS) is a disease caused by human immunodeficiency virus (HIV) that leads to a progressive deterioration of the immune system. Mother-to-child transmission of HIV is a problem in Nigeria where its rate has been on an increase over the past few years. The Exponentiation family is one of the most efficient methods proposed and studied for introducing skewness and flexibility into continuous probability distributions with a single shape parameter. In this paper, the method of exponentiation has been used to add flexibility to the exponential inverse exponential distribution which results to a new continuous model known as “Exponentiated Exponential Inverse Exponential distribution”. The properties, application and estimation of parameters of the new distribution using the method of maximum likelihood estimation are presented and discussed in this paper. The new model has been applied to a dataset on the rate of mother-to-child transmission of HIV and the result is being compared among the fitted distributions using some information criteria.