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

2022 ◽  
Author(s):  
Tamás Jónás ◽  
Christophe Chesneau ◽  
József Dombi ◽  
Hassan Salah Bakouch
Keyword(s):  
Exponential Distribution ◽  
Stochastic Ordering ◽  
Quantile Function ◽  
Reliability Theory ◽  
Truncated Distribution ◽  
Survival Times ◽  
Rate Functions ◽  
Inverse Exponential Distribution ◽  
Two Parameter ◽  
Skewness And Kurtosis

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.

scholarly journals Reliability Analysis of the New Exponential Inverted Topp–Leone Distribution with Applications

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1662
Author(s):  
Ahmed Sayed M. Metwally ◽  
Amal S. Hassan ◽  
Ehab M. Almetwally ◽  
B M Golam Kibria ◽  
Hisham M. Almongy
Keyword(s):  
Reliability Analysis ◽  
Confidence Intervals ◽  
Hazard Rate ◽  
Shape Parameter ◽  
Quantile Function ◽  
Proposed Model ◽  
Distribution Parameters ◽  
Rate Functions ◽  
New Distribution ◽  
Skewness And Kurtosis

The inverted Topp–Leone distribution is a new, appealing model for reliability analysis. In this paper, a new distribution, named new exponential inverted Topp–Leone (NEITL) is presented, which adds an extra shape parameter to the inverted Topp–Leone distribution. The graphical representations of its density, survival, and hazard rate functions are provided. The following properties are explored: quantile function, mixture representation, entropies, moments, and stress–strength reliability. We plotted the skewness and kurtosis measures of the proposed model based on the quantiles. Three different estimation procedures are suggested to estimate the distribution parameters, reliability, and hazard rate functions, along with their confidence intervals. Additionally, stress–strength reliability estimators for the NEITL model were obtained. To illustrate the findings of the paper, two real datasets on engineering and medical fields have been analyzed.

scholarly journals A New Generalized Transmuted Inverse Exponential Distribution: Properties and Application

2018 ◽  
pp. 1-13
Author(s):  
Uchenna U. Uwadi ◽  
Elebe E. Nwaezza
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Real Life Data ◽  
Proposed Model ◽  
Inverse Exponential Distribution ◽  
The Moment

In this study, we proposed a new generalised transmuted inverse exponential distribution with three parameters and have transmuted inverse exponential and inverse exponential distributions as sub models. The hazard function of the distribution is nonmonotonic, unimodal and inverted bathtub shaped making it suitable for modelling lifetime data. We derived the moment, moment generating function, quantile function, maximum likelihood estimates of the parameters, Renyi entropy and order statistics of the distribution. A real life data set is used to illustrate the usefulness of the proposed model.     

scholarly journals On the Extended Generalized Inverse Exponential Distribution with Its Applications

2020 ◽  
pp. 14-27
Author(s):  
Sule Ibrahim ◽  
Bello Olalekan Akanji ◽  
Lawal Hammed Olanrewaju
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Generalized Inverse ◽  
Real Data ◽  
Quantile Function ◽  
Exponential Model ◽  
Data Sets ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Inverse Exponential Distribution

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.

scholarly journals Characterizations of the Beta Kumaraswamy Exponential Distribution

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 23
Author(s):  
Zakeia A. Al-saiary ◽  
Rana A. Bakoban ◽  
Areej A. Al-zahrani
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Hazard Function ◽  
Real Data ◽  
Quantile Function ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Data Set ◽  
Skewness And Kurtosis

In this article, the five-parameter beta Kumaraswamy exponential distribution (BKw-E) is introduced, and some characterizations of this distribution are obtained. The shape of the hazard function and some other important properties—such as median, mode, quantile function, and mean—are studied. In addition, the moments, skewness, and kurtosis are found. Furthermore, important measures such as Rényi entropy and order statistics are obtained; these have applications in many fields. An example of a real data set is discussed.

scholarly journals A New Extended Generalized Inverse Exponential Distribution: Properties and Applications

2021 ◽  
pp. 30-46
Author(s):  
Bashiru Omeiza Sule
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Generalized Inverse ◽  
Real Life ◽  
Quantile Function ◽  
Exponential Model ◽  
Rate Function ◽  
Data Sets ◽  
Competing Models ◽  
Inverse Exponential Distribution

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.

Characterizing the Exponential Law Under Laplace Order Domination

1995 ◽  
Vol 45 (3-4) ◽  
pp. 171-178 ◽  
Author(s):  
Murari Mitra ◽  
Sujit K. Basu ◽  
M. C. Bhattacharjee
Keyword(s):  
Exponential Distribution ◽  
Reliability Theory ◽  
Subject Classification ◽  
Exponential Law ◽  
Life Distributions

Interesting characterizations of the exponential distribution have been obtained in classes of life distributions important in reliability theory. The results strengthen some of the analogous conclusions already existing in the literature. AMS (1991) Subject Classification No. Primary 62NOS: Secondaey 90825. 60F99.

scholarly journals Transmuted Mukherjee-Islam Distribution: A Generalization of Mukherjee-Islam Distribution

2017 ◽  
Vol 9 (4) ◽  
pp. 135
Author(s):  
Loai M. A. Al-Zou'bi
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Continuous Distribution ◽  
Quantile Function ◽  
Descriptive Statistics ◽  
Likelihood Method ◽  
Distribution Parameters ◽  
Rate Functions ◽  
Mean Variance ◽  
New Distribution

A new continuous distribution is proposed in this paper. This distribution is a generalization of Mukherjee-Islam distribution using the quadratic rank transmutation map. It is called transmuted Mukherjee-Islam distribution (TMID). We have studied many properties of the new distribution: Reliability and hazard rate functions. The descriptive statistics: mean, variance, skewness, kurtosis are also studied. Maximum likelihood method is used to estimate the distribution parameters. Order statistics and Renyi and Tsallis entropies were also calculated. Furthermore, the quantile function and the median are calculated.

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