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 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 Kumaraswamy Distribution Based on Alpha Power Transformation Methods

2021 ◽  
pp. 14-29
Author(s):  
H. E. Hozaien ◽  
G. R. AL Dayian ◽  
A. A. EL-Helbawy
Keyword(s):  
Residual Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Mean Residual Life ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Data Set ◽  
Kumaraswamy Distribution

In this paper, the alpha power Kumaraswamy distribution, new alpha power transformed Kumaraswamy distribution and new extended alpha power transformed Kumaraswamy distribution are presented. Some statistical properties of the three distributions are derived including quantile function, moments and moment generating function, mean residual life and order statistics. Estimation of the unknown parameters based on maximum likelihood estimation are obtained. A simulation study is carried out. Finally, a real data set is applied.

scholarly journals A Distribution for Instantaneous Failures

Stats ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 247-258 ◽  
Author(s):  
Pedro L. Ramos ◽  
Francisco Louzada
Keyword(s):  
Residual Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Mean Residual Life ◽  
Parameter Distribution ◽  
Coverage Probabilities ◽  
Instantaneous Failures ◽  
The Relationship ◽  
Mean Variance ◽  
New Distribution

A new one-parameter distribution is proposed in this paper. The new distribution allows for the occurrence of instantaneous failures (inliers) that are natural in many areas. Closed-form expressions are obtained for the moments, mean, variance, a coefficient of variation, skewness, kurtosis, and mean residual life. The relationship between the new distribution with the exponential and Lindley distributions is presented. The new distribution can be viewed as a combination of a reparametrized version of the Zakerzadeh and Dolati distribution with a particular case of the gamma model and the occurrence of zero value. The parameter estimation is discussed under the method of moments and the maximum likelihood estimation. A simulation study is performed to verify the efficiency of both estimation methods by computing the bias, mean squared errors, and coverage probabilities. The superiority of the proposed distribution and some of its concurrent distributions are tested by analyzing four real lifetime datasets.

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 Fisher consistent estimation of regression parameter in the proportional mean residual life model with frailty

Ekonomia ◽  
2021 ◽  
Vol 27 (2) ◽  
pp. 81-88
Author(s):  
Magdalena Skolimowska-Kulig
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Regression Models ◽  
Residual Life ◽  
Likelihood Estimation ◽  
Mean Residual Life ◽  
Regression Parameter ◽  
Consistent Estimation ◽  
Regression Parameters ◽  
Life Model

In the article, we consider the Fisher consistent estimation of the regression parameters in the proportional mean residual life model with arbitrary frailty. It is discussed that conventional estimation procedures, such as the maximum likelihood estimation or Cox’s approach, which are employed in common regression models, may also yield consistent inference in the extended models.

scholarly journals A zero truncated discrete distribution: Theory and applications to count data

2020 ◽  
pp. 167-190
Author(s):  
Tassaddaq Hussain Kiani
Keyword(s):  
Count Data ◽  
Negative Binomial ◽  
Residual Life ◽  
Probability Generating Function ◽  
Strength Parameter ◽  
Mean Residual Life ◽  
Factorial Moments ◽  
Residual Life Function ◽  
Collective Risk Model ◽  
Life Function

The analysis and modeling of zero truncated count data is of primary interest in many elds such as engineering, public health, sociology, psychology, epidemiology. Therefore, in this article we have proposed a new and simple structure model, named a zero truncated discrete Lindley distribution. Thedistribution contains some submodels and represents a two-component mixture of a zero truncated geometric distribution and a zero truncated negative binomial distribution with certain parameters. Several properties of the distribution are obtained such as mean residual life function, probability generating function, factorial moments, negative moments, moments of residual life function, Bonferroni and Lorenz curves, estimation of parameters, Shannon and Renyi entropies, order statistics with the asymptotic distribution of their extremes and range, a characterization, stochastic ordering and stress-strength parameter. Moreover, the collective risk model is discussed by considering theproposed distribution as primary distribution and exponential and Erlang distributions as secondary ones. Test and evaluation statistics as well as three real data applications are considered to assess the peformance of the distribution among the most frequently zero truncated discrete probability models.

scholarly journals A Lomax-inverse Lindley Distribution: Model, Properties and Applications to Lifetime Data

2019 ◽  
pp. 1-28
Author(s):  
Terna Godfrey Ieren ◽  
Peter Oluwaseun Koleoso ◽  
Adana’a Felix Chama ◽  
Innocent Boyle Eraikhuemen ◽  
Nasiru Yakubu
Keyword(s):  
Likelihood Estimation ◽  
Quantile Function ◽  
Distribution Model ◽  
Lindley Distribution ◽  
Limiting Behavior ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Inverse Lindley Distribution ◽  
New Distribution ◽  
Better Than

This article proposed a new extension of the Inverse Lindley distribution called “Lomax-Inverse Lindley distribution” which is more flexible compared to the Inverse Lindley distribution and other similar models. The paper derives and discusses some Statistical properties of the new distribution which include the limiting behavior, quantile function, reliability functions and distribution of order statistics. The parameters of the new model are estimated by method of maximum likelihood estimation. Conclusively, three lifetime datasets were used to evaluate the usefulness of the proposed model and the results indicate that the proposed extension is more flexible and performs better than the other distributions considered in this study.

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 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.

scholarly journals The Exponentiated Lindley Geometric Distribution with Applications

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 510
Author(s):  
Bo Peng ◽  
Zhengqiu Xu ◽  
Min Wang
Keyword(s):  
Maximum Likelihood ◽  
Geometric Distribution ◽  
Residual Life ◽  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters

We introduce a new three-parameter lifetime distribution, the exponentiated Lindley geometric distribution, which exhibits increasing, decreasing, unimodal, and bathtub shaped hazard rates. We provide statistical properties of the new distribution, including shape of the probability density function, hazard rate function, quantile function, order statistics, moments, residual life function, mean deviations, Bonferroni and Lorenz curves, and entropies. We use maximum likelihood estimation of the unknown parameters, and an Expectation-Maximization algorithm is also developed to find the maximum likelihood estimates. The Fisher information matrix is provided to construct the asymptotic confidence intervals. Finally, two real-data examples are analyzed for illustrative purposes.

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