Exponentiated Gamma Distribution Research Articles

Exponentiated gamma constant-stress partially accelerated life tests with unified hybrid censored data: Statistical inferences

This study considers one of the partially accelerated life testing models, mainly a constant-stress approach with unified hybrid censored data. The data represents the lifetime of units following the exponentiated gamma distribution (EGD). The estimation techniques for the parameter of EGD and the acceleration factor are discussed, along with the maximum likelihood estimation technique, the Bayesian and E-Bayesian estimation. Utilizing the squared error loss (SEL) and LINEX loss functions, the E-Bayesian and Bayesian estimates are generated. For deriving the estimates of Bayesian and E-Bayesian approaches, we use the MCMC method. Real-world data is also provided for illustration. Furthermore, unified hybrid censoring schemes (HCSs) are examined to determine their effectiveness in the light of the results. In the end, we compare among the proposed methods during their findings. The study's findings demonstrate how well the suggested techniques work when utilizing unified HCS. The study also makes clear how important it is to adopt the CSPALT model, as it yields more failed things in a shorter amount of time than items with typical use situations. In conclusion, it is suggested that this research be used to tasks like industrial product reliability testing.

Chi-squared type test for distributional censored and uncensored validity with numerical assessments and real data applications

AbstractIn this work, we introduce a new chi-squared type test the odd Lindley exponentiated gamma distribution. The new test is an extension of the Nikulin–Rao–Robson test. The new test is tailored to fit the right censored data. The performance of the new test, as well as the baseline Nikulin–Rao–Robson test, are evaluated via numerical simulation. The new test, as well as the baseline Nikulin–Rao–Robson test, are also evaluated using the data. Furthermore, we present some characterization results.

The exponentiated new exponential-gamma distribution: Properties and applications

The exponentiated new exponential-gamma distribution: Properties and applications

Analysis of information measures using generalized type-Ⅰ hybrid censored data

<abstract><p>An entropy measure of uncertainty has a complementary dual function called extropy. In the last six years, this measure of randomness has gotten a lot of attention. It cannot, however, be applied to systems that have survived for some time. As a result, the idea of residual extropy was created. To estimate the extropy and residual extropy, Bayesian and non-Bayesian estimators of unknown parameters of the exponentiated gamma distribution are generated. Bayesian estimators are regarded using balanced loss functions like the balanced squared error, balanced linear exponential and balanced general entropy. We use the Lindley method to get the extropy and residual extropy estimates for the exponentiated gamma distribution based on generalized type-Ⅰ hybrid censored data. To test the effectiveness of the proposed methodologies, a simulation experiment was carried out, and the actual data set was studied for illustrative purposes. In summary, the mean squared error values decrease as the number of failures increases, according to the results obtained. The Bayesian estimates of residual extropy under the balanced linear exponential loss function perform well compared to the other estimates. Alternatively, the Bayesian estimates of the extropy perform well under a balanced general entropy loss function in the majority of situations.</p></abstract>

An Extension of Exponentiated Gamma Distribution: A New Regression Model with Application

An Extension of Exponentiated Gamma Distribution: A New Regression Model with Application

Usual stochastic ordering of the sample maxima from dependent distribution‐free random variables

In this paper, we discuss stochastic comparison of the largest order statistics arising from two sets of dependent distribution‐free random variables with respect to multivariate chain majorization, where the dependency structure can be defined by Archimedean copulas. When a distribution‐free model with possibly two parameter vectors has its matrix of parameters changing to another matrix of parameters in a certain mathematical sense, we obtain the first sample maxima is larger than the second sample maxima with respect to the usual stochastic order, based on certain conditions. Applications of our results for scale proportional reverse hazards model, exponentiated gamma distribution, Gompertz–Makeham distribution, and location‐scale model, are also given. Meanwhile, we provide two numerical examples to illustrate the results established here.

Modeling Covid-19 Deaths in Nigeria Using Exponential-Gamma Distribution

This work examines the performance of Exponential-Gamma distribution and the existing Exponetial and Gamma in relative to the distribution that will best fit the data on Covid-19 death in Nigeria from March 2020 to April 2021. The parameters of the distribution were estimated using the method of maximum likelihood estimates. The newly developed Exponential-Gamma distribution was compared with the exiting Exponential and Gamma distributions using the log-likelihood function, Akaike information criterion (AIC), and Bayesian information criterion (BIC) as the criteria for selecting the best fit model. The results show that the newly developed Exponential-Gamma distribution performed better than the existing Exponential and Gamma distributions in contrast in terms of model fit, this showed that the newly developed Exponential-Gamma distribution is more flexible and precise in analyzing the Covid-19 data other than the existing Exponential and Gamma distributions.

Modeling Covid-19 Deaths in Nigeria Using Exponential-Gamma Distribution

Modeling Covid-19 Deaths in Nigeria Using Exponential-Gamma Distribution

Marshall olkin extended exponentiated Gamma distribution and its applications

Different methods for obtaining new probability distributions have been introduced in the literature in recent years, for example, (Gupta et al., 1998) proposed an interesting uni-parametric lifetime distribution, Exponentiated Gamma (EG), which hazard function has increasing and bathtub shapes. In this paper, we build a new two-parameters distribution, the Marshall Olkin Extended Exponentiated Gamma (MOEEG) distribution, which is derived from the Marshall-Olkin method and the EG distribution. The hazard function of this new distribution can accommodate monotonic, non-monotonic and unimodal shapes, allowing a better fit to greater data variability. In addition to the great flexibility of fitting the data, it contains only two parameters providing a simple parameter estimation procedure, unlike other distributions proposed in the literature that have three or more parameters. Some properties of the new distribution considered in this paper are presented such as n-th time, r-th moment of residual life, r-thmoment of residual life inverted, stochastic ordering, entropy, mean deviation, Bonferroni and Lorenz curve, skewness, kurtosis, order statistics, and stress-strength parameter. We also apply two different estimation methods, maximum likelihood and Bayesian approach. Real data applications are presented to illustrate the usefulness of this new distribution.

Inferences for Exponentiated Gamma Constant-Stress Partially Accelerated Life Test Model Based on Generalized Type-I Hybrid Censored Data

In this paper, the exponentiated gamma distribution (EGD) with generalized Type-I hybrid censored data under constant-stress partially accelerated life test (CSPALT) model is considered. The Bayesian and E-Bayesian estimation methods, as well as the maximum likelihood estimation method, are discussed for the parameter of the distribution and the acceleration factor. The E-Bayesian and Bayesian estimates are derived by using the squared error loss (SEL) and the LINEX loss functions. The MCMC method is applied for deriving the Bayesian and then E-Bayesian estimates. Moreover, a real data set is given for the illustrative purpose. After all, an evaluation is performed for the results of the proposed methods.

A STOCHASTIC MODEL FOR ESTIMATION OF EXPECTED TIME TO RECRUITMENT WHEN THE THRESHOLD HAS GENERALIZED EXPONENTIATED GAMMA DISTRIBUTION

In any organization a number of factors are required to generate production activities and the manpower is the most vital factor. The manpower requirements may increase in course of time due to increase in production activities or due to depletion of manpower at random time points. Hence recruitment is to be made whenever the total demands for manpower crosses the so called threshold level. In this paper an estimate of the expected time to recruitment is derived under the assumption that the threshold level is a random variable which follows the Generalized Exponentiated Gamma distribution. The variances also found out. The results are substantiated with numerical examples

MLE-Based Parameter Estimation for Four-Parameter Exponential Gamma Distribution and Asymptotic Variance of Its Quantiles

The choice of a probability distribution function and confidence interval of estimated design values have long been of interest in flood frequency analysis. Although the four-parameter exponential gamma (FPEG) distribution has been developed for application in hydrology, its maximum likelihood estimation (MLE)-based parameter estimation method and asymptotic variance of its quantiles have not been well documented. In this study, the MLE method was used to estimate the parameters and confidence intervals of quantiles of the FPEG distribution. This method entails parameter estimation and asymptotic variances of quantile estimators. The parameter estimation consisted of a set of four equations which, after algebraic simplification, were solved using a three dimensional Levenberg-Marquardt algorithm. Based on sample information matrix and Fisher’s expected information matrix, derivatives of the design quantile with respect to the parameters were derived. The method of estimation was applied to annual precipitation data from the Weihe watershed, China and confidence intervals for quantiles were determined. Results showed that the FPEG was a good candidate to model annual precipitation data and can provide guidance for estimating design values.

Bayesian Estimation for Exponentiated Gamma Distribution Under Progressive Type-II Censoring Using Different Approximation Techniques

In this paper, we proposed the Bayesian estimation of the parameter and reliability function in exponentiated gamma distribution under progressive type-II censored samples. The Bayes estimates of the parameter and reliability function are derived under the assumption of independent gamma prior by three different methods namely Lindley's approximation, Tierney-Kadane and Markov Chain Monte Carlo methods. Further, the comparison of Bayes estimators with corresponding maximum likelihood estimators have been done through simulation study. Finally, a real data set has been used to illustrate the above study in realistic phenomenon.

Secure hybrid satellite-UWOC cooperative relaying system under malicious unmanned aerial vehicle eavesdropper threat

In this paper, the secrecy performance of a hybrid satellite-Underwater Optical Communication (UWOC) system in the presence of an Unmanned Aerial Vehicle (UAV) eavesdropper is investigated. The satellite and eavesdropper Radio Frequency (RF) links are respectively subjected to Shadowed-Rician and Nakagami-m fading distributions whereas the UWOC link experiences mixed Exponential-Gamma distribution under difference detection schemes such as heterodyne detection and Intensity Modulation with Direct Detection (IM/DD). Specifically, the equivalent Cumulative Distribution Function (CDF) closed-form expression of the concerned system is then obtained. Based on this, the analytical closed-form expressions of the system Connection Outage Probability (COP), Secrecy Outage Probability (SOP), Strictly Positive Secrecy Capacity (SPSC) and Average Secrecy Capacity (ASC) are derived. By our findings, it is found that the satellite shadowing effect, air bubbles level and temperature gradients and eavesdropper distance significantly have impact on the system secrecy performance. The result also illustrated that the heterodyne detection outperforms the IM/DD under the system and channel conditions. Finally, the accuracy of the analytical expressions is justified through Monte-Carlo simulations.

Poly-Weighted Exponentiated Gamma Distribution with Application

This paper proposes a weighting of the exponentiated gamma distribution with a polynomial function called the poly-weighted exponentiated gamma distribution (PWEGD). It shows that the modified distribution harnesses the multi-dimensional effects of the distribution. We provided an extensive mathematical treatment of this proposed distribution: obtained its parameters, estimated its statistical properties with applicable, tests and compared the estimates with existing distribution. The study estimated the cumulative distribution function, hazard function, survival function, skewness, kurtosis, mode, median and quartiles of the distribution and evaluated the distribution with Monte Carlo simulated data and the data of the wind direction (degrees) in Lagos, Nigeria. Empirical analysis showed that with increased polynomial function, the estimates and the statistical properties like the expectation, variance, standard error, median, mode, hazard and survival functions, cumulative distribution function (CDF), moments, skewness and kurtosis were significantly better than the existing root distributions. The MSE of the parameters decreased with increased power and the parameter is significant (p <0.05). It is concluded that the proposed distribution does not only provide better fitting but also establishes an efficient structure for lifetime data modelling.

Modified Average Sample Number for Improved Double Sampling Plan Based on Truncated Life Test Using Exponentiated Distributions

The reliability of the product has developed a dynamic issue in a worldwide business market. Generally acceptance sampling guarantees the superiority of the product. In acceptance sampling plan, increasing the sample size may lead to minimization of customers' risk of accepting bad lots and producers' risk of rejecting good lots to a certain level but will increase the cost of inspection. Hence truncation of life test time may be introduced to reduce the cost of inspection. Modified Average Sample Number (MASN) for Improved Double Sampling Plan (IDSP) based on truncated life test for popular exponentiated family such as exponentiated gamma, exponentiated lomax and exonentiated Weibull distribution are considered. The modified ASN creates a band width for average sample number which is much useful for the consumer and producer. The interval for average sample number makes the choice of consumer with a maximum and minimum sample size which is of much benefit without any loss for the producer. The probability of acceptance and average sample number based on modified double sampling plan for lower and upper limit is computed for the exponentiated family. Optimal parameters of IDSP under various exponentiated families with different shape parameters were computed. The proposed plan is compared over traditional double sampling and modified double sampling using Gamma distribution, Weibull distribution and Birnbaum-Saunders distribution and shows that the proposed plan with respect to exponentiated family performs better than all other plans. The tables were provided for all distributions. Comparative study of tables based on proposed exponentiated family and earlier existing plan are also done.

A New Mixture of Exponential-Gamma Distribution

A new distribution called New Mixture of Exponential-Gamma Distribution is presented in this paper. This new distribution contains exponential and standardized Lindley distributions as sub models. Some of the structural properties of the proposed distribution which include the survival function, hazard rate function, moments, moment generating function, quantile function, distribution of order statistics and Renyi entropy are obtained. The maximum likelihood method of estimation was used to estimate the parameters of the distribution. A Simulation study was carried out to examine the performance and accuracy of the maximum likelihood estimates of the proposed distribution. An application of the proposed distribution to two real lifetime datasets is presented to illustrate its usefulness and superiority over some existing related models.

Estimating the Performance Measure of Exponential-Gamma Distribution with Application to Failure Rate Data

Estimating the Performance Measure of Exponential-Gamma Distribution with Application to Failure Rate Data

ON STUDY OF EXPONENTIATED GAMMA DISTRIBUTION BASED ON UNIFIED HYBRID CENSORED DATA

In this article, we will study the estimation of the unknown parameters for exponentiated gamma distribution as well as a survival function, failure rate function and the coefficient of variation based on unified hybrid censored data. In addition that, we will study maximum likelihood and Bayesian estimates. To calculate the Bayes estimates of the model parameters will beused Markov chain Monte Carlo method (MCMC). Gibbs within the Metropolis-Hasting algorithm has been applied to generate MCMC samples from the posterior density function and calculate approximate confidence intervals for the unknown parameters, survival, failure rate functions and coefficient of variation. All resultsobtained are based on the balanced-squared error loss, balanced linear-exponential loss, and balanced general entropy loss functions. At the end of article, real data has been used to determine how the estimation method can be used in practice.

The Inverted Exponentiated Gamma Distribution: A Heavy-Tailed Model with Upside Down Bathtub Shaped Hazard Rate

In this article, we proposed and studied the inverted exponentiated gamma distribution (IEGD). IEGD is obtained by considering the inverse transformation of exponentiated gamma variate. This distribution has been motivated by the extensive use of the exponentiated gamma model in many applied areas and also due to the fact that this new generalization provides more flexibility to analyze real data with upside down bathtub (UBT) hazard rate. The shape of the distribution has been traced mathematically and found that the proposed model is compatible with UBT hazard rate models. The tail area property is also presented based on the idea of Marshall and Olkin (2007) and it is concluded that the new model belongs to the family of heavy-tailed distributions. Some other characteristics such as reliability, hazard, the quantile function, skewness and kurtosis, stochastic ordering, stress-strength reliability and order statistics have been explicitly derived. The classical and Bayesian estimation procedures have been discussed to estimate the unknown parameter of IEGD. The performances of classical and Bayes estimators are studied in terms of average mean square error (MSE) by conducting Monte Carlo simulations. Finally, a real data set with UBT type hazard rate is analyzed for the illustrative purpose of the study.