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.

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 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.

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.

A FINITE RANGE DISCRETE LIFE DISTRIBUTION

1995 ◽  
Vol 02 (02) ◽  
pp. 147-160 ◽  
Author(s):  
C.D. LAI ◽  
D.Q. WANG
Keyword(s):  
Failure Time ◽  
Residual Life ◽  
Discrete Distribution ◽  
Lifetime Distribution ◽  
Mortality Data ◽  
Mean Residual Life ◽  
Life Distribution ◽  
Life Data ◽  
Proposed Model ◽  
Two Parameter

Discrete life data arise in many practical situations and even for continuous data we may find cases where the data are presented in grouped form, so that a discrete model can be used. In this paper, we propose a new two-parameter discrete lifetime distribution for modeling this type of data. The distribution under consideration has some interesting ageing properties; in particular, it is able to describe bathtub-shaped failure rate as well as upside-down bathtub-shaped mean residual life. We use this discrete distribution to model Halley’s mortality data and find it fits reasonably well. The proposed model, though quite simple in appearance, is flexible and potentially useful in describing various types of failure time. Some analytical results will also be presented.

scholarly journals A GENERALIZATION OF SUJATHA DISTRIBUTION AND ITS APPLICATIONS WITH REAL LIFETIME DATA

2017 ◽  
Vol 22 (1) ◽  
pp. 66-83 ◽  
Author(s):  
Rama Shanker ◽  
Kamlesh Kumar Shukla ◽  
Hagos Fesshaye
Keyword(s):  
Residual Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Stochastic Ordering ◽  
Rate Function ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Lorenz Curves ◽  
Two Parameter ◽  
Life Function

A two-parameter generalization of Sujatha distribution (AGSD), which includes Lindley distribution and Sujatha distribution as particular cases, has been proposed. It's important mathematical and statistical properties including its shape for varying values of parameters, moments, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviations, Bonferroni and Lorenz curves, and stress-strength reliability have been discussed. Maximum likelihood estimation method has been discussed for estimating its parameters. AGSD provides better fit than Sujatha, Aradhana, Lindley and exponential distributions for modeling real lifetime data.Journal of Institute of Science and TechnologyVolume 22, Issue 1, July 2017, Page: 66-83

scholarly journals Logit Truncated-Exponential Skew-Logistic Distribution with Properties and Applications

Modelling ◽  
2021 ◽  
Vol 2 (4) ◽  
pp. 776-794
Author(s):  
Liyuan Pang ◽  
Weizhong Tian ◽  
Tingting Tong ◽  
Xiangfei Chen
Keyword(s):  
Residual Life ◽  
Real Data ◽  
Interval Data ◽  
Quantile Function ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Unknown Parameters ◽  
Bounded Interval

In recent years, bounded distributions have attracted extensive attention. At the same time, various areas involve bounded interval data, such as proportion and ratio. In this paper, we propose a new bounded model, named logistic Truncated exponential skew logistic distribution. Some basic statistical properties of the proposed distribution are studied, including moments, mean residual life function, Renyi entropy, mean deviation, order statistics, exponential family, and quantile function. The maximum likelihood method is used to estimate the unknown parameters of the proposed distribution. More importantly, the applications to three real data sets mainly from the field of engineering science prove that the logistic Truncated exponential skew logistic distribution fits better than other bounded distributions.

scholarly journals A New Skewed Discrete Model: Properties, Inference, and Applications

2021 ◽  
pp. 799-816
Author(s):  
Ahmed Z. Afify ◽  
Mahmoud Elmorshedy ◽  
M. S. Eliwa
Keyword(s):  
Biological Sciences ◽  
Residual Life ◽  
Risk Measures ◽  
Discrete Distribution ◽  
Real Data ◽  
Mass Function ◽  
Rate Function ◽  
Estimation Methods ◽  
Mean Residual Life ◽  
Probability Mass Function

In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass function and an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distribution including the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and L- moment statistics have been established. Two actuarial or risk measures were derived. The numerical computations for these measures are conducted for several parametric values of the model parameter. The parameter of the introduced distribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conducted to explore the performance of the studied estimators. The performance of the proposed distribution has been examined by three over-dispersed real data sets from biological sciences.

scholarly journals A Two-parameter Rama Distribution

2019 ◽  
pp. 365-382
Author(s):  
U. Umeh Edith ◽  
T. Umeokeke Ebele ◽  
A. Ibenegbu Henrietta
Keyword(s):  
Goodness Of Fit ◽  
Residual Life ◽  
Real Life ◽  
Stochastic Ordering ◽  
Rate Function ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Estimation Of Parameters ◽  
Lorenz Curves ◽  
Two Parameter

In this paper, a two-parameter Rama distribution is proposed. This is coined from Lindley distribution and Rama distribution. Its mathematical and statistical properties which include its shapes, moment, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviation; Bonferroni and Lorenz curves are also discussed. The estimation of parameters has been X-rayed using methods of moment and maximum likelihood. Also AIC and BIC are used to test for the goodness of fit of the model which is applied to a real life data of hepatitis B patients. This new distribution is compared with Rama, 2-parameter Akash, 2-parameter Lindley, Akash, Shanker, Ishita, Lindley and Exponential distributions in order to determine the efficiency of the new model.

scholarly journals A New Five Parameter Lifetime Distribution: Properties and Application

2017 ◽  
Vol 13 (3) ◽  
pp. 7205-7218
Author(s):  
Shimaa A. Dessoky ◽  
Ahmed M. T. Abd El-Bar
Keyword(s):  
Hazard Rate ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rate Function ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Hazard Rate Function ◽  
Unknown Parameters ◽  
Data Set ◽  
Present Distribution

This paper deals with a new generalization of the Weibull distribution. This distribution is called exponentiated exponentiated exponential-Weibull (EEE-W) distribution. Various structural properties of the new probabilistic model are considered, such as hazard rate function, moments, moment generating function, quantile function, skewness, kurtosis, Shannon entropy and Rényi entropy. The maximum likelihood estimates of its unknown parameters are obtained. Finally, areal data set is analyzed and it observed that the present distribution can provide a better fit than some other known distributions.

A Two-Parameter Pranav Distribution with Properties and Its Application.

2019 ◽  
Author(s):  
Edith Umeh ◽  
Amuche Ibenegbu
Keyword(s):  
Goodness Of Fit ◽  
Residual Life ◽  
Real Life ◽  
Lifetime Distribution ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Hypertensive Patients ◽  
Study Results ◽  
Two Parameter

Introduction: Lifetime distribution has drawn so much attention in recent research, and this has lead to the development of new lifetime distribution. Addition of parameters to the existing distribution makes the distribution more flexible and reliable and applicable model has become the focus of the recent search. This paper proposed a two-parameter Pranav distribution which has its base from a one-parameter Pranav and Ishita distribution. Methods Two parameter Pranav distribution was proposed. Mathematical and statistical properties of the distribution which includes; moments, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviation, Bonferroni and Lorenz curves were developed. Other lifetime distributions such as Ishita, Akash, Sujatha, Shanker, Lindley, and Exponential distributions were considered in the study. Results: This new distribution was compared with two-parameter Akash, Lindley, one parameter Pranav, Ishita, Akash, Sujatha, Shanker, Lindley, and Exponential distributions to determine the efficiency of the new model. The estimation of parameters has been X-rayed using the method of moments and maximum likelihood. Also, AIC and BIC were used to test for the goodness of fit of the model which was applied to a real-life data of hypertensive patients. The results show that the new two-parameter Pranav distribution has the lowest value of AIC and BIC Conclusion: Based on the AIC and BIC values we can conclude that the two-parameter Pranav is more efficient than the other distribution for modeling survival of hypertensive patients. Hence two-parameter Pranav can be seen as an important distribution in modeling lifetime data.

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