scholarly journals Application to Engineering and Medical Data Using Three-Parameter Exponential Model

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Waleed Almutiry ◽  
Amani Abdullah Alahmadi ◽  
Ibrahim Elbatal ◽  
Ibrahim E. Ragab ◽  
Oluwafemi Samson Balogun ◽  
...  
Keyword(s):  
Simulation Analysis ◽  
Residual Life ◽  
Quantile Function ◽  
Exponential Model ◽  
Statistical Characteristics ◽  
Mean Residual Life ◽  
New Model ◽  
Conditional Moments ◽  
Mean Inactivity Time ◽  
Real World Datasets

This paper is devoted to a new lifetime distribution having three parameters by compound the exponential model and the transmuted Topp-Leone-G. The new proposed model is called the transmuted Topp-Leone exponential model; it is useful in lifetime data and reliability. The new model is very flexible; its pdf can be right skewness, unimodal, and decreasing shaped, but the hrf of the suggested model can be unimodal, constant, and decreasing. Numerous statistical characteristics of the new model, notably the quantile function, moments, incomplete moments, conditional moments, mean residual life, mean inactivity time, and entropy are produced and investigated. The system’s parameters are estimated using the maximum likelihood approach. All estimators should be theoretically convergent, which is supported by a simulation analysis. Finally, two real-world datasets from the engineering and medical disciplines explore the new model’s relevance and adaptability in comparison to the alternatives models such as the beta exponential, the Marshall–Olkin generalized exponential, the exponentiated Weibull, the modified Weibull, and the transmuted Burr type X models.

scholarly journals The Kumaraswamy Pareto IV Distribution

2021 ◽  
Vol 50 (5) ◽  
pp. 1-22
Author(s):  
Muhammad Hussain Tahir ◽  
Gauss M. Cordeiro ◽  
Muhammad Mansoor ◽  
Muhammad Zubair ◽  
Ayman Alzaatreh
Keyword(s):  
Density Function ◽  
Residual Life ◽  
Information Matrix ◽  
Real Life ◽  
Quantile Function ◽  
Mean Residual Life ◽  
Model Parameters ◽  
New Model ◽  
Lorenz Curves ◽  
Mean Waiting Time

We introduce a new model named the Kumaraswamy Pareto IV distribution which extends the Pareto and Pareto IV distributions. The density function is very flexible and can be left-skewed, right-skewed and symmetrical shapes. It hasincreasing, decreasing, upside-down bathtub, bathtub, J and reversed-J shaped hazard rate shapes. Various structural properties are derived including explicit expressions for the quantile function, ordinary and incomplete moments,Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, probability weighted moments and generating function. We provide the density function of the order statistics and their moments. The Renyi and q entropies are also obtained. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new model is illustrated by means of three real-life data sets. In fact, our proposed model provides a better fit to these data than the gamma-Pareto IV, gamma-Pareto, beta-Pareto,exponentiated Pareto and Pareto IV models.

A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations

2021 ◽  
Vol 71 (4) ◽  
pp. 983-1004
Author(s):  
Majid Hashempour
Keyword(s):  
Residual Life ◽  
Real Data ◽  
Quantile Function ◽  
Rate Function ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Residual Entropy ◽  
Mean Residual Life ◽  
Conditional Moments ◽  
Two Parameter

Abstract In this paper, we introduce a new two-parameter lifetime distribution which is called extended Half-Logistic (EHL) distribution. Theoretical properties of this model including the hazard function, quantile function, asymptotic, extreme value, moments, conditional moments, mean residual life, mean past lifetime, residual entropy, cumulative residual entropy and order statistics are derived and studied in details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two real data sets are illustration the purposes.

SOME RESULTS ABOUT MIT ORDER AND IMIT CLASS OF LIFE DISTRIBUTIONS

2006 ◽  
Vol 20 (3) ◽  
pp. 481-496 ◽  
Author(s):  
Xiaohu Li ◽  
Maochao Xu
Keyword(s):  
Renewal Process ◽  
Residual Life ◽  
Random Time ◽  
Mean Residual Life ◽  
Stochastic Comparisons ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
Life Distributions ◽  
Preservation Property

We investigate some new properties of mean inactivity time (MIT) order and increasing MIT (IMIT) class of life distributions. The preservation property of MIT order under increasing and concave transformations, reversed preservation properties of MIT order, and IMIT class of life distributions under the taking of maximum are developed. Based on the residual life at a random time and the excess lifetime in a renewal process, stochastic comparisons of both IMIT and decreasing mean residual life distributions are conducted as well.

scholarly journals Extended Poisson Lomax Distribution

2020 ◽  
pp. 461-470
Author(s):  
Mohamed Sowilem Hamed
Keyword(s):  
Generating Function ◽  
Random Number ◽  
Residual Life ◽  
Random Number Generation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
New Model ◽  
Lomax Distribution ◽  
Number Generation

The main goal of this article is to introduce a new extension of the continuous Lomax distribution with a strong physical motivation. Some of its statistical properties such as moments, incomplete moments, moment generating function, quantile function, random number generation, quantile spread ordering and moment of the reversed residual life are derived. Two applications are provided to illustrate the importance and flexibility of the new model.

scholarly journals The Beta Exponential Fréchet Distribution with Applications

2017 ◽  
Vol 46 (1) ◽  
pp. 41-63 ◽  
Author(s):  
M.E. Mead ◽  
Ahmed Z. Afify ◽  
G.G. Hamedani ◽  
Indranil Ghosh
Keyword(s):  
Residual Life ◽  
Real Data ◽  
Mean Residual Life ◽  
Model Parameters ◽  
Data Sets ◽  
Nested Models ◽  
Fréchet Distribution ◽  
Proposed Model ◽  
Mean Inactivity Time ◽  
Frechet Distribution

We define and study a new generalization of the Fréchet distribution called the beta exponential Fréchet distribution. The new model includes thirty two special models. Some of its mathematical properties, including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean residual life, mean inactivity time, order statistics and entropies are derived. The method of maximum likelihood is proposed to estimate the model parameters. A small simulation study is alsoreported. Two real data sets are applied to illustrate the flexibility of the proposed model compared with some nested and non-nested models.

scholarly journals The Half-Logistic Lomax Distribution for Lifetime Modeling

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Masood Anwar ◽  
Jawaria Zahoor
Keyword(s):  
Maximum Likelihood ◽  
Residual Life ◽  
Information Matrix ◽  
Simulated Data ◽  
Quantile Function ◽  
Rate Function ◽  
Mean Residual Life ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Proposed Model

We introduce a new two-parameter lifetime distribution called the half-logistic Lomax (HLL) distribution. The proposed distribution is obtained by compounding half-logistic and Lomax distributions. We derive some mathematical properties of the proposed distribution such as the survival and hazard rate function, quantile function, mode, median, moments and moment generating functions, mean deviations from mean and median, mean residual life function, order statistics, and entropies. The estimation of parameters is performed by maximum likelihood and the formulas for the elements of the Fisher information matrix are provided. A simulation study is run to assess the performance of maximum-likelihood estimators (MLEs). The flexibility and potentiality of the proposed model are illustrated by means of real and simulated data sets.

scholarly journals A New Lifetime Distribution: Properties, Copulas, Applications, and Different Classical Estimation Methods

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Naif Alotaibi
Keyword(s):  
Least Square ◽  
Estimation Methods ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Least Square Estimation ◽  
New Model ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
The Mean ◽  
Anderson Darling

A new continuous version of the inverse flexible Weibull model is proposed and studied. Some of its properties such as quantile function, moments and generating functions, incomplete moments, mean deviation, Lorenz and Bonferroni curves, the mean residual life function, the mean inactivity time, and the strong mean inactivity time are derived. The failure rate of the new model can be “increasing-constant,” “bathtub-constant,” “bathtub,” “constant,” “J-HRF,” “upside down bathtub,” “increasing,” “upside down-increasing-constant,” and “upside down.” Different copulas are used for deriving many bivariate and multivariate type extensions. Different non-Bayesian well-known estimation methods under uncensored scheme are considered and discussed such as the maximum likelihood estimation, Anderson Darling estimation, ordinary least square estimation, Cramér-von-Mises estimation, weighted least square estimation, and right tail Anderson Darling estimation methods. Simulation studies are performed for comparing these estimation methods. Finally, two real datasets are analyzed to illustrate the importance of the new model.

scholarly journals Estimation of Sine Inverse Exponential Model under Censored Schemes

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
M. Shrahili ◽  
I. Elbatal ◽  
Waleed Almutiry ◽  
Mohammed Elgarhy
Keyword(s):  
Hazard Rate ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Fitting ◽  
Exponential Model ◽  
Rate Function ◽  
Numerical Results ◽  
Conditional Moments ◽  
Censored Samples ◽  
Distribution Parameters

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.

scholarly journals A Novel Method for Developing Efficient Probability Distributions with Applications to Engineering and Life Science Data

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Alamgir Khalil ◽  
Abdullah Ali H. Ahmadini ◽  
Muhammad Ali ◽  
Wali Khan Mashwani ◽  
Shokrya S. Alshqaq ◽  
...  
Keyword(s):  
Residual Life ◽  
Probability Distributions ◽  
Probability Model ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Strength Parameter ◽  
Mean Residual Life ◽  
Simulation Studies ◽  
Science Data ◽  
Proposed Model

In this paper, a new approach for deriving continuous probability distributions is developed by incorporating an extra parameter to the existing distributions. Frechet distribution is used as a submodel for an illustration to have a new continuous probability model, termed as modified Frechet (MF) distribution. Several important statistical properties such as moments, order statistics, quantile function, stress-strength parameter, mean residual life function, and mode have been derived for the proposed distribution. In order to estimate the parameters of MF distribution, the maximum likelihood estimation (MLE) method is used. To evaluate the performance of the proposed model, two real datasets are considered. Simulation studies have been carried out to investigate the performance of the parameters’ estimates. The results based on the real datasets and simulation studies provide evidence of better performance of the suggested distribution.

scholarly journals A New Compound Version of the Generalized Lomax Distribution for Modeling Failure and Service Times

2020 ◽  
pp. 95-107 ◽  
Author(s):  
S. Ansari ◽  
Rezk H. ◽  
Haitham Yousof
Keyword(s):  
Generating Function ◽  
Random Number ◽  
Residual Life ◽  
Random Number Generation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
New Model ◽  
Lomax Distribution ◽  
Number Generation

The main goal of this article is to introduce a new extension of the continuous Lomax distribution with a strong physical motivation. Some of its statistical properties such as moments, incomplete moments, moment generating function, quantile function, random number generation, quantile spread ordering and moment of the reversed residual life are derived. Two applications are provided to illustrate the importance and flexibility of the new model.

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