Inverse Exponential Distribution Research Articles

Parameter estimation of inverse exponential Rayleigh distribution based on classical methods

This paper introduces and developed a new lifetime distribution known as inverse exponential Rayleigh distribution (IERD). The new two-scale parameters generalized distribution was studies with its distribution and density functions, besides that the basic properties such as survival, hazard, cumulative hazard, quantile function, skewness, and Kurtosis functions were established and derived. To estimate the model parameters, maximum likelihood, and rank set sampling estimation methods were applied with real-life data.

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.

Parameter Estimation of Alpha Power Inverted Topp-Leone Distribution with Applications

We introduce a new two-parameter lifetime model, referred to alpha power transformed inverted Topp-Leone, derived by combining the alpha power transformation-G family with the inverted Topp-Leone distribution. Structural properties of the proposed distribution are implemented like; quantile function, residual and reversed residual life, Rényi entropy measure, moments and incomplete moments. The maximum likelihood, weighted least squares, maximum product of spacing, and Bayesian methods of estimation are considered. A simulation study is worked out to evaluate the restricted sample properties of the proposed distribution. Numerical results showed that the Bayesian estimates give more accurate results than the corresponding other estimates in the majority of the situations. The flexibility of the suggested model is demonstrated given some applications related to reliability, medicine, and engineering. A real data set is used to illustrate the potentiality of the alpha power transformed inverted Topp-Leone distribution compared to inverted Topp-Leone, inverse Weibull, alpha power inverse Weibull, inverse Lomax, alpha power inverse Lomax, inverse exponential, and alpha power exponential distributions. Criteria measures and their results showed that the suggested distribution is the best candidate for the considered data sets. The alpha power transformed inverted Topp-Leone distribution operates well for lifetime modeling.

Entropy Bayesian Analysis for the Generalized Inverse Exponential Distribution Based on URRSS

Entropy Bayesian Analysis for the Generalized Inverse Exponential Distribution Based on URRSS

Odd Lomax Inverse Exponential Distribution: Model, Properties and Applications

A new distribution; Odd Lomax Inverse Exponential distribution with three parameters and consistent unimodal failure rate is proposed. Structural properties of the new distribution namely; ordinary moments, quantile and generating functions, entropy measurements, order statistics and other useful measures were obtained. The model parameters were estimated using the method of maximum likelihood. The usefulness of the new distribution was proven empirically using two real datasets

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.

The Inverse-Power Logistic-Exponential Distribution: Properties, Estimation Methods, and Application to Insurance Data

The present paper proposes a new distribution called the inverse power logistic exponential distribution that extends the inverse Weibull, inverse logistic exponential, inverse Rayleigh, and inverse exponential distributions. The proposed model accommodates symmetrical, right-skewed, left-skewed, reversed-J-shaped, and J-shaped densities and increasing, unimodal, decreasing, reversed-J-shaped, and J-shaped hazard rates. We derive some mathematical properties of the proposed model. The model parameters were estimated using five estimation methods including the maximum likelihood, Anderson–Darling, least-squares, Cramér–von Mises, and weighted least-squares estimation methods. The performance of these estimation methods was assessed by a detailed simulation study. Furthermore, the flexibility of the introduced model was studied using an insurance real dataset, showing that the proposed model can be used to fit the insurance data as compared with twelve competing models.

Assessing the effect of E-Bayesian inference for Poisson inverse exponential distribution parameters under different loss functions and its application

This paper present E-Bayesian and Bayesian estimators of parameters of Poisson inverse exponential distribution (PIED) under Squared error loss function (SELF), General entropy loss function (GELF) and Linear Exponential loss function (LINEX) for progressive type-II censored data with binomial removals (PT-II CBRs). The E-Bayesian and corresponding Bayesian estimators are compared in terms of their risks based on simulated samples from PIED. The proposed methodology is applied to survival time of multiple myeloma patients data.

English

English

STATISTICAL PROPERTIES OF LOMAX-INVERSE EXPONENTIAL DISTRIBUTION AND APPLICATIONS TO REAL LIFE DATA

This paper proposes a Lomax-inverse exponential distribution as an improvement on the inverse exponential distribution in the form of Lomax-inverse Exponential using the Lomax generator (Lomax-G family) with two extra parameters to generalize any continuous distribution (CDF). The probability density function (PDF) and cumulative distribution function (CDF) of the Lomax-inverse exponential distribution are defined. Some basic properties of the new distribution are derived and extensively studied. The unknown parameters estimation of the distribution is done by method of maximum likelihood estimation. Three real-life datasets are used to assess the performance of the proposed probability distribution in comparison with some other generalizations of Lomax distribution. It is observed that Lomax-inverse exponential distribution is more robust than the competing distributions, inverse exponential and Lomax distributions. This is an evident that the Lomax generator is a good probability model.

Conditional Probabilities of Hellenic Arc Earthquakes Based on Different Distribution Models

The 27 November 2019 Mw 6.0 earthquake that occurred in the southwestern part of the Hellenic Arc near Crete Island provided evidence of the high potential for strong earthquakes and active seismicity in the Hellenic Arc. In addition, tsunamis have been reported to occur for the region after major earthquakes in the historical past, so the seismic hazard of the Hellenic Arc should be evaluated in detail. The aim of this study is to evaluate the seismic hazard of the Hellenic Arc more reliably and accurately by estimating the conditional probabilities of a strong earthquake based on Weibull, gamma, log-normal, exponential, Rayleigh, and inverse Gaussian distribution models for the inter-event time of Mw ≥ 6.0 earthquakes that occurred between 1900 and 2019 in the study area. The fit between each model and the data was tested using four different test criteria, namely the log-likelihood value, Akaike information criterion, Bayesian information criteria, and Kolmogorov–Smirnov test. According to the results, the inverse Gaussian distribution was selected as the best, the log-normal distribution as the second best, the Weibull and gamma distributions as intermediate, and the Rayleigh and exponential distribution as the poorest and second poorest model, respectively. The conditional probability of an earthquake with magnitude Mw ≥ 6.0 is estimated to be higher than 0.70 according to all of the models used in this study for the base year te = 0 (te = 2015) and t > 5 years (t > 2020). Moreover, the results obtained based on the inverse Gaussian, exponential, log-normal, and Weibull distribution models are close to each other and are higher than 0.60 for te = 0 and t ≥ 3 years (t ≥ 2018). The outcomes of this study when using the different distribution models will contribute to assessments of the seismic as well as tsunami hazards for the region.

A Note on Topp-Leone Odd Log-Logistic Inverse Exponential Distribution

The inverse exponential distribution is widely used in the field of reliability. In this article, we present a generalization of the inverse exponential distribution in formation of Topp-Leone odd log-logistic inverse exponential distribution. We provide a comprehensive account of some mathematical properties of the Topp-Leone odd log-logistic inverse exponential distribution. The possible shapes of the corresponding probability density function and hazard function are obtained and graphical demonstration are presented. The distribution is found to be unimodal. The results for moment, moment-generating function, and probability-generating function are computed. The residual and reversed residual functions are also obtained. The proposed method of maximum likelihood is used for the estimation of model parameters. The performance of the parameters is investigated through simulation. The usefulness of the proposed model is illustrated by means of a real data set.

On the Extended Generalized Inverse Exponential Distribution with Its Applications

We propose a new distribution called the extended generalized inverse exponential distribution with four positive parameters, which extends the 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 and odd functions. The method of maximum likelihood is used to estimate the parameters of the distribution. We illustrate its potentiality with applications to two real data sets which show that the extended generalized inverse exponential model provides a better fit than other models considered.

On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions

This paper develops the exponentiated Mfamily of continuous distributions, aiming to provide new statistical models for data fitting purposes. It stands out from the other families, as it depends on two baseline distributions, with the use of ratio and power transforms in the definition of the main cumulative distribution function. Thanks to the joint action of the possibly different baseline distributions, flexible statistical models can be created, motivating a complete study in this regard. Thus, we discuss the theoretical properties of the new family, with emphasis on those of potential interest to the overall probability and statistics. Then, a new three-parameter lifetime distribution is derived, with the choices of the inverse exponential and exponential distributions as baselines. After pointing out the great flexibility of the related model, we apply it to analyze an actual dataset of current interest: the daily COVID-19 cases observed in Pakistan from 21 March to 29 May 2020 (inclusive). As notable results, we demonstrate that the proposed model is the best among the 15 top ranked models in the literature, including the inverse exponential and exponential models, several modern extensions of them depending on more parameters, and the “unexponentiated” version of the proposed model as well. As future perspectives, the proposed model can be of interest to analyze data on COVID-19 cases in other countries, for possible comparison studies.

Bayesian and Maximum Likelihood Estimation of the Shape Parameter of Exponential Inverse Exponential Distribution: A Comparative Approach

This paper aims at making Bayesian analysis on the shape parameter of the exponential inverse exponential distribution using informative and non-informative priors. Bayesian estimation was carried out through a Monte Carlo study under 10,000 replications. To assess the effects of the assumed prior distributions and loss function on the Bayesian estimators, the mean square error has been used as a criterion. Overall, simulation results indicate that Bayesian estimation under QLF outperforms the maximum likelihood estimation and Bayesian estimation under alternative loss functions irrespective of the nature of the prior and the sample size. Also, for large sample sizes, all methods perform equally well.

On A Shape Parameter of Gompertz Inverse Exponential Distribution Using Classical and Non Classical Methods of Estimation

The Gompertz inverse exponential distribution is a three-parameter lifetime model with greater flexibility and performance for analyzing real life data. It has one scale parameter and two shape parameters responsible for the flexibility of the distribution. Despite the importance and necessity of parameter estimation in model fitting and application, it has not been established that a particular estimation method is better for any of these three parameters of the Gompertz inverse exponential distribution. This article focuses on the development of Bayesian estimators for a shape of the Gompertz inverse exponential distribution using two non-informative prior distributions (Jeffery and Uniform) and one informative prior distribution (Gamma prior) under Square error loss function (SELF), Quadratic loss function (QLF) and Precautionary loss function (PLF). These results are compared with the maximum likelihood counterpart using Monte Carlo simulations. Our results indicate that Bayesian estimators under Quadratic loss function (QLF) with any of the three prior distributions provide the smallest mean square error for all sample sizes and different values of parameters.

Type II Power Topp-Leone Generated Family of Distributions with Statistical Inference and Applications

In this paper, we present and study a new family of continuous distributions, called the type II power Topp-Leone-G family. It provides a natural extension of the so-called type II Topp-Leone-G family, thanks to the use of an additional shape parameter. We determine the main properties of the new family, showing how they depend on the involving parameters. The following points are investigated: shapes and asymptotes of some important functions, quantile function, some mixture representations, moments and derivations, stochastic ordering, reliability and order statistics. Then, a special model of the family based on the inverse exponential distribution is introduced. It is of particular interest because the related probability functions are tractable and possess various kinds of asymmetric shapes. Specially, reverse J, left skewed, near symmetrical and right skewed shapes are observed for the corresponding probability density function. The estimation of the model parameters is performed by the use of three different methods. A complete simulation study is proposed to illustrate their numerical efficiency. The considered model is also applied to analyze two different kinds of data sets. We show that it outperforms other well-known models defined with the same baseline distribution, proving its high level of adaptability in the context of data analysis.

On the Flexibility of Topp Leone Exponentiated Inverse Exponential Distribution

In this paper, we introduced a new continuous probability distribution called the Topp Leone exponentiated inverse exponential distribution with three parameters. We studied the nature of proposed distribution with the help of its mathematical and statistical properties such as quantile function, ordinary moments, moment generating function, survival function and hazard function. The probability density function of order statistic for this distribution was also obtained. We performed classical estimation of parameters by using the technique of maximum likelihood estimate. The proposed model was applied to two real-life datasets. The first data set has to do with patients with cancer of tongue with aneuploidy DNA profile and the second data set has to do with patients who were diagnosed with hypertension and received at least one treatment related to hypertension. The results showed that the new distribution provided better fit than other distributions presented. As such, it can be categorically said that the Topp Leone exponentiated inverse exponential distribution is good distribution in modeling survival data.

Likelihood-based inference for the ratio of the parameters of the inverse exponential distributions

Likelihood-based inference for the ratio of the parameters of the inverse exponential distributions