Inverse Exponential Research Articles

Some Properties and Applications of the Gompertz Topp-Leone Inverse Exponential Distribution

The Gompertz Topp Leone Inverse Exponential (GoTLIE) distribution, which has three parameters, is a novel distribution that we introduce in this article. Inverse exponential (IE) distributions with various parameter values can be combined to form the new distribution. The moments, moment generating function, quantile function, reliability function, and hazard function are only a few of the crucial structural aspects of the new model that are derived. We utilize the approach of greatest likelihood to estimate the new distribution's parameters (MLE). To show how flexible the new distribution is, we utilized two real data used to demonstrate the GoTLIE distribution.

On the study of the recurrence relations and characterizations based on progressive first-failure censoring

<abstract> <p>In this research, the progressive first-failure censored data (PFFC) from the Kumaraswamy modified inverse-Weibull distribution (KMIWD) were used to obtain the recurrence relations and characterizations for single and product moments. The recurrence relationships allow for a rapid and efficient assessment of the means, variances and covariances for any sample size. Additionally, the paper outcomes can be boiled down to the traditional progressive type-II censoring. Also, some special cases are limited to some lifetime distributions as the exponentiated modified inverse Weibull and Kumaraswamy inverse exponential.</p> </abstract>

On the Distribution of the Product of Inverse Pareto and Exponential Random Variables

This article considers Inverse Pareto and Exponential distributions to create the distribution of the product. The researchers derived its properties, such as; survival functions and hazard functions, and used the model criterion such as Sum Square Error (SSE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) in estimating the parameters for deriving the best joint distribution between monthly precipitation and temperature in the Philippines from 1974 to 2013. The results showed that considering the monthly precipitation and temperature data, the distribution of the product of Inverse Pareto and Exponential outperformed the other existing distribution of the product.

Gamma Generalized Extended Inverse Exponential Distribution: A Novel Distribution in Modeling COVID-19 Cases in Nigerian Africa: A Personal Perspective

In this study, we developed a novel distribution called Gamma Inverse Exponential (GIE) distribution, which has proved to be a more flexible distribution in modeling COVID-19 case fatality in Nigeria. We studied some statistical properties of the new distribution, which include: moments, incomplete moments, quantile function, Renyi entropy, and mean deviation. A real-life data application to a number of reported cases of COVID-19 infection between March 2019 to 2021 shows that the GIE distribution has a better fit than some competing distributions in fitting the data. Time series analysis of the COVID-19 data is also considered.

Inverse Two-Parameter Lindley Distribution and Its Applications

This paper proposes an Inverse two-parameter Lindley distribution (ITPLD). This is originated from Lindley distribution and two-parameter Lindley distribution. Its mathematical and statistical properties which includes its survival function, hazard rate function, shape characteristics of the density, stochastic ordering, entropy measure, and stress-strength reliability were discussed. The estimation of parameters was carried out using the method of maximum likelihood. Also, in the application of the model, HQIC, BIC, CAIC, AIC, and K.S are used to test for the goodness of fit of the model which was applied to two real data sets. The Inverse two-parameter Lindley distribution was compared with Inverse Lindley, Inverse Akash, and Inverse Exponential distributions in order to determine its superiority.

Bayesian Estimation of the Parameters of the Odd Generalized Exponentiated - Inverse Exponential Distribution (OGE -IED)

The Odd Generalized Exponentiated-Inverse Exponential Distribution, a three parameter distribution, is a hybrid of the Generalized Exponential distribution. Each of the parameters were assigned a gamma prior independently resulting to a posterior distribution that is mathematically intractable impossible to obtain marginal posterior distribution for two of the parameters, and a likelihood function that is not known traditionally to R or other statistical software. Resort was made to STAN in order to obtain Bayesian estimates - leveraging on STAN’s provision for user-defined distribution functions. Two datasets were used; remission times (in months) of bladder cancer patients and COVID-19 Survey data in Andalusia, Spain. In the end, the Maximum Likelihood estimates maximized the likelihood more than the Bayesian estimates - though with a slight margin of not more than 0.77. On the other hand, the Bayesian estimates proved to be more stable yielding very negligible standard errors compared to the Maximum Likelihood estimates.

Lomax gamble type two distributions with applications to lifetime data

The Gumbel Type-Two (GTT) distribution among many classical distributions has been found to lack the capacity to adequately fit some random phenomenon due to its monotonic failure rates thereby limiting its application. The Lomax-Generator was employed in this study to generalize the GTT distribution in order to derive the Lomax Gumbel Type-Two (LGTT) distribution capable of providing better modeling fits to real dataset. The new distribution has the Lomax Inverse Exponential distribution as a special case; the reliability and hazard rates functions were investigated. The distribution is unimodal, positively skewed and close to bell shape depending on parameter values. The quantile, median and order statistics were derived while the method of maximum likelihood estimation was used for estimating the parameters of the distribution. The proposed distribution demonstrated its potentials for modeling events whose distributions tends to be platykurtic, leptokurtic and approximately symmetric. Two lifetime survival datasets were analyzed using the distribution and results revealed the importance of application of LGTT distribution to the datasets with superior modeling fits than other four generalizations of GTT distributions existing in literatures derived using other generator. Three additional real life datasets were also used to compare the performance of LGTT with some distributions derived using Lomax as generator, results of analysis revealed that LGTT exhibits greater flexible potentials for modelling the real life datasets.

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.

Estimation of Sine Inverse Exponential Model under Censored Schemes

In this article, we introduce a new one-parameter model, which is named sine inverted exponential (SIE) distribution. The SIE distribution is a new extension of the inverse exponential (IE) distribution. The SIE distribution aims to provide the SIE model for data-fitting purposes. The SIE distribution is more flexible than the inverted exponential (IE) model, and it has many applications in physics, medicine, engineering, nanophysics, and nanoscience. The density function (PDFu) of SIE distribution can be unimodel shape and right skewed shape. The hazard rate function (HRFu) of SIE distribution can be J-shaped and increasing shaped. We investigated some fundamental statistical properties such as quantile function (QFu), moments (Mo), moment generating function (MGFu), incomplete moments (ICMo), conditional moments (CMo), and the SIE distribution parameters were estimated using the maximum likelihood (ML) method for estimation under censored samples (CS). Finally, the numerical results were investigated to evaluate the flexibility of the new model. The SIE distribution and the IE distribution are compared using two real datasets. The numerical results show the superiority of the SIE distribution.

T-Inverse Exponential Family Of Distributions

Recently, several methods have been introduced to generate neoteric distributions with more exibility, like T-X, T-R [Y] and alpha power. The T-Inverse exponential [Y] neoteric family of distributons is proposed in this paper utilising the T-R [Y] method. A generalised inverse exponential (IE) distribution family has been established. The distribution family is generated using quantile functions of some dierent distributions. A number of general features in the T-IE [Y] family are examined, like mean deviation, mode, moments, quantile function, and entropies. A special model of the T-IE [Y] distribution family was one of those old distributions. Certain distribution examples are produced by the T-IE [Y] family. An applied case was presented which showed the importance of the neoteric family.

APPLICATIONS OF INVERSE WEIBULL RAYLEIGH DISTRIBUTION TO FAILURE RATES AND VINYL CHLORIDE DATA SETS

In this work, a new three parameter distribution called the Inverse Weibull Rayleigh distribution is proposed. Some of its statistical properties were presented. The PDF plot of Inverse Weibull Rayleigh distribution showed that it is good for modeling positively skewed and symmetrical datasets. The plot of the hazard function showed that the proposed distribution can fit datasets with bathtub shape. Method of maximum likelihood estimation was employed to estimate the parameters of the distribution, the estimators of the parameters of Inverse Weibull Rayleigh distribution is asymptotically unbiased and asymptotically efficient from the result of the simulation carried out. Applying the new distribution to a positively skewed Vinyl Chloride data set shows that the distribution performs better than Rayleigh, Generalized Rayleigh, Weibull Rayleigh, Inverse Weibull, Inverse Weibull Weibull, Inverse Weibull Inverse Exponential and Inverse Weibull Pareto distribution in fitting the data as it has the smallest AIC value. Also, applying the new distribution to a negatively skewed bathtub shape failure rates data shows that the distribution is a competitive model after Weibull Rayleigh and Inverse Weibull Weibull distributions in fitting the data because it has the third least AIC value.

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.

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 Odd Generalized NH Inverse Exponential Model: Theory and Application

In this paper we introduce a new lifetime distribution derived from odd generalized NH-G (OGNH-G) family technique called OGNH-inverse exponential (OGNHIE) distribution. We establish various mathematical properties. The maximum likelihood (ML) estimates for the OGNHIE parameters are derived. Finally the model is applied to a real dataset. We apply goodness of fit statistics and graphical tools to examine the adequacy of the OGNHIE distribution. The importance of this research lies in deriving a new distribution under the name OGNHIE, which is considered the best distributions in analyzing data of life times at present if compared to many distribution in analysis real data.

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.

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 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.

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English

Weighted Version of Generalized Inverse Weibull Distribution

Weighted distributions are used in many fields, such as medicine, ecology, and reliability. A weighted version of the generalized inverse Weibull distribution, known as weighted generalized inverse Weibull distribution (WGIWD), is proposed. Basic properties including mode, moments, moment generating function, skewness, kurtosis, and Shannon’s entropy are studied. The usefulness of the new model was demonstrated by applying it to a real-life data set. The WGIWD fits better than its submodels, such as length biased generalized inverse Weibull (LGIW), generalized inverse Weibull (GIW), inverse Weibull (IW) and inverse exponential (IE) distributions.