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

2021 ◽  
pp. 12-30
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Gerald Ikechukwu Onwuka ◽  
Bassa Shiwaye Yakura ◽  
Hassan Allahde
Keyword(s):  
Infant Mortality ◽  
Exponential Distribution ◽  
Hiv Transmission ◽  
Transmission Rate ◽  
Probability Distributions ◽  
Real Life ◽  
Information Criteria ◽  
Infant Mortality Rate ◽  
Unknown Parameters ◽  
Inverse Exponential Distribution

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.

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

2020 ◽  
pp. 68-81
Author(s):  
Abraham Iorkaa Asongo ◽  
Innocent Boyle Eraikhuemen ◽  
Adamu Abubakar Umar ◽  
Terna Godfrey Ieren
Keyword(s):  
Exponential Distribution ◽  
Transmission Rate ◽  
Immune Deficiency Syndrome ◽  
Continuous Model ◽  
Information Criteria ◽  
Mother To Child Transmission ◽  
Estimation Of Parameters ◽  
Child Transmission ◽  
Inverse Exponential Distribution ◽  
Mother To Child

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.

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

2020 ◽  
Vol 4 (2) ◽  
pp. 680-694
Author(s):  
Dr. Sauta Saidu Abdulkadir ◽  
J. Jerry ◽  
T. G. Ieren
Keyword(s):  
Exponential Distribution ◽  
Probability Model ◽  
Continuous Distribution ◽  
Real Life ◽  
Likelihood Estimation ◽  
Parameters Estimation ◽  
Cumulative Distribution ◽  
Unknown Parameters ◽  
Real Life Data ◽  
Inverse Exponential Distribution

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.

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 The Maxwell – Exponential Distribution: Theory and Application to Lifetime Data

2021 ◽  
Vol 3 (2) ◽  
pp. 65-80
Author(s):  
Usman Aliyu Abdullahi ◽  
Ahmad Abubakar Suleiman ◽  
Aliyu Ismail Ishaq ◽  
Abubakar Usman ◽  
Aminu Suleiman
Keyword(s):  
Exponential Distribution ◽  
Survival Function ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Information Criteria ◽  
Cumulative Distribution ◽  
Two Parameters ◽  
Maximum Likelihood Estimation Method

Two parameters Maxwell – Exponential distribution was proposed using the Maxwell generalized family of distribution. The probability density function, cumulative distribution function, survival function, hazard function, quantile function, and statistical properties of the proposed distribution are discussed. The parameters of the proposed distribution have been estimated using the maximum likelihood estimation method. The potentiality of the estimators was shown using a simulation study. The overall assessment of the performance of Maxwell - Exponential distribution was determined by using two real-life datasets. Our findings reveal that the Maxwell – Exponential distribution is more flexible compared to other competing distributions as it has the least value of information criteria.

scholarly journals Bayesian Change Point Estimation Based on Masked Data in Exponential Distribution Parallel System

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Exponential Distribution ◽  
Gibbs Sampling ◽  
Change Point ◽  
Latent Variables ◽  
Likelihood Function ◽  
Probability Distributions ◽  
Qualitative Change ◽  
Parallel System ◽  
Point Estimation ◽  
Unknown Parameters

Change point reflects a qualitative change in things. It has gained some applications in the field of reliability. In order to estimate the position parameters of the change point, a Bayesian change point model based on masked data and Gibbs sampling was proposed. By filling in missing lifetime data and introducing latent variables, the simple likelihood function is obtained for exponential distribution parallel system under censored data. This paper describes the probability distributions and random generation methods of the missing lifetime variables and latent variables, and obtains the full conditional distributions of the change point position parameters and other unknown parameters. By Gibbs sampling and estimation of unknown parameters, the estimates of the mean, median, and quantile of the parameter posterior distribution are obtained. The specific steps of Gibbs sampling are introduced in detail. The convergence of Gibbs sampling is also diagnosed. Random simulation results show that the estimations are fairly accurate.

scholarly journals A Study on Properties and Applications of a Lomax Gompertz-Makeham Distribution

2019 ◽  
pp. 1-27
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Terna Godfrey Ieren ◽  
Tajan Mashingil Mabur ◽  
Mohammed Sa’ad ◽  
Samson Kuje ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Probability Distributions ◽  
Real Life ◽  
Likelihood Estimation ◽  
The Other ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Compound Model ◽  
New Distribution

The article presents an extension of the Gompertz-Makeham distribution using the Lomax generator of probability distributions. This generalization of the Gompertz-Makeham distribution provides a more skewed and flexible compound model called Lomax Gompertz-Makeham distribution. The paper derives and discusses some Mathematical and Statistical properties of the new distribution. The unknown parameters of the new model are estimated via the method of maximum likelihood estimation. In conclusion, the new distribution is applied to two real life datasets together with two other related models to check its flexibility or performance and the results indicate that the proposed extension is more flexible compared to the other two distributions considered in the paper based on the two datasets used.

scholarly journals On the Properties and Applications of a Transmuted Lindley-Exponential Distribution

2019 ◽  
pp. 1-13
Author(s):  
Adamu Abubakar Umar ◽  
Innocent Boyle Eraikhuemen ◽  
Peter Oluwaseun Koleoso ◽  
Jerry Joel ◽  
Terna Godfrey Ieren
Keyword(s):  
Exponential Distribution ◽  
Continuous Distribution ◽  
Real Life ◽  
Likelihood Estimation ◽  
Good Evidence ◽  
Survival Times ◽  
Probability Models ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Better Than

The Quadratic rank transmutation map proposed for introducing skewness and flexibility into probability models with a single parameter known as the transmuted parameter has been used by several authors and is proven to be useful. This article uses this method to add flexibility to the Lindley-Exponential distribution which results to a new continuous distribution called “transmuted Lindley-Exponential distribution”. This paper presents the definition, validation, properties, application and estimation of unknown parameters of the transmuted Lindley-Exponential distribution using the method of maximum likelihood estimation. The new distribution has been applied to a real life dataset on the survival times (in days) of 72 guinea pigs and the result gives good evidence that the transmuted Lindley-Exponential distribution is better than the Lindley-Exponential distribution, Exponential distribution and Lindley distribution based on the dataset used.

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

2020 ◽  
pp. 1-10
Author(s):  
Terna Godfrey Ieren ◽  
Adana’a Felix Chama ◽  
Olateju Alao Bamigbala ◽  
Jerry Joel ◽  
Felix M. Kromtit ◽  
...  
Keyword(s):  
Exponential Distribution ◽  
Loss Function ◽  
Real Life ◽  
Quadratic Loss ◽  
Prior Distributions ◽  
Quadratic Loss Function ◽  
Informative Prior ◽  
Informative Prior Distribution ◽  
Inverse Exponential Distribution ◽  
Bayesian Estimators

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.

scholarly journals Odd Lindley-Rayleigh Distribution: Its Properties and Applications to Simulated and Real Life Datasets

2020 ◽  
pp. 63-88
Author(s):  
Terna Godfrey Ieren ◽  
Sauta Saidu Abdulkadir ◽  
Adekunle Abdulmumeen Issa
Keyword(s):  
Real Life ◽  
Rayleigh Distribution ◽  
Information Criteria ◽  
The Other ◽  
Cumulative Distribution ◽  
Parameter Estimates ◽  
Probability Models ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Two Parameters

This article develops an extension of the Rayleigh distribution with two parameters and greater flexibility which is an improvement over Lindley distribution, Rayleigh distribution and other generalizations of the Rayleigh distribution. The new model is known as “odd Lindley-Rayleigh Distribution”. The definitions of its probability density function and cumulative distribution function using the odd Lindley-G family of distributions are provided. Some properties of the new distribution are also derived and studied in this article with applications and discussions. The estimation of the unknown parameters of the proposed distribution is also carried out using the method of maximum likelihood. The performance of the proposed probability distribution is compared to some other generalizations of the Rayleigh distribution using three simulated datasets and a real life dataset. The results obtained are compared using the values of some information criteria evaluated with the parameter estimates of the fitted distributions based on the four datasets and it is revealed that the proposed distribution outperforms all the other fitted distributions. This performance has shown that the odd Lindley-G family of distribution is an adequate generator of probability models and that the odd Linley-Rayleigh distribution is a very flexible distribution for fitting different kinds of datasets better than the other generalizations of the Rayleigh distribution considered in this study.

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