In this paper, we introduce a class of Lindley and Weibull distributions (LW) that are useful for modeling lifetime data with a comprehensive mathematical treatment. The new class of generated distributions includes s...In this paper, we introduce a class of Lindley and Weibull distributions (LW) that are useful for modeling lifetime data with a comprehensive mathematical treatment. The new class of generated distributions includes some well-known distributions, such as exponential, gamma, Weibull, Lindley, inverse gamma, inverse Weibull, inverse Lindley, and others. We provide closed-form expressions for the density, cumulative distribution, survival function, hazard rate function, moments, moments generating function, quantile, and stochastic orderings. Moreover, we discuss maximum likelihood estimation and the algorithm for computing the parameters estimates. Some sub models are discussed as an illustration with real data sets to show the flexibility of this class.展开更多
In this paper, a two-parameter Lindley distribution, of which the one parameter Lindley distribution (LD) is a particular case, for modeling waiting and survival times data has been introduced. Its moments, failure ra...In this paper, a two-parameter Lindley distribution, of which the one parameter Lindley distribution (LD) is a particular case, for modeling waiting and survival times data has been introduced. Its moments, failure rate function, mean residual life function, and stochastic orderings have been discussed. It is found that the expressions for failure rate function mean residual life function and stochastic orderings of the two-parameter LD shows flexibility over one-parameter LD and exponential distribution. The maximum likelihood method and the method of moments have been discussed for estimating its parameters. The distribution has been fitted to some data-sets relating to waiting times and survival times to test its goodness of fit to which earlier the one parameter LD has been fitted by others and it is found that to almost all these data-sets the two parameter LD distribution provides closer fits than those by the one parameter LD.展开更多
In this paper, we introduce a new extension of the power Lindley distribution, called the exponentiated generalized power Lindley distribution. Several mathematical properties of the new model such as the shapes of th...In this paper, we introduce a new extension of the power Lindley distribution, called the exponentiated generalized power Lindley distribution. Several mathematical properties of the new model such as the shapes of the density and hazard rate functions, the quantile function, moments, mean deviations, Bonferroni and Lorenz curves and order statistics are derived. Moreover, we discuss the parameter estimation of the new distribution using the maximum likelihood and diagonally weighted least squares methods. A simulation study is performed to evaluate the estimators. We use two real data sets to illustrate the applicability of the new model. Empirical findings show that the proposed model provides better fits than some other well-known extensions of Lindley distributions.展开更多
We proposed </span><span style="font-family:Verdana;">“</span><span style="font-family:Verdana;">a new extension of three</span><span style="font-family:Verda...We proposed </span><span style="font-family:Verdana;">“</span><span style="font-family:Verdana;">a new extension of three</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">parametric distribution” called the inverse power two-parameter weighted Lindley (IPWL) distribution capable of modeling a upside-down bathtub hazard rate function. This distribution is studied to get basic structural properties such as reliability measures, moments, inverse moments and its related measures. Simulation studies </span><span style="font-family:Verdana;">are </span><span style="font-family:Verdana;">done to present the performance and behavior of maximum likelihood estimates of the IPWL distribution parameters. Finally, we perform goodness of fit measures and test statistics using a real data set to show the performance of the new distribution.展开更多
An important property that any lifetime model should satisfy is scale invariance.In this paper,a new scale-invariant quasi-inverse Lindley(QIL)model is presented and studied.Its basic properties,including moments,quan...An important property that any lifetime model should satisfy is scale invariance.In this paper,a new scale-invariant quasi-inverse Lindley(QIL)model is presented and studied.Its basic properties,including moments,quantiles,skewness,kurtosis,and Lorenz curve,have been investigated.In addition,the well-known dynamic reliability measures,such as failure rate(FR),reversed failure rate(RFR),mean residual life(MRL),mean inactivity time(MIT),quantile residual life(QRL),and quantile inactivity time(QIT)are discussed.The FR function considers the decreasing or upside-down bathtub-shaped,and the MRL and median residual lifetime may have a bathtub-shaped form.The parameters of the model are estimated by applying the maximum likelihood method and the expectation-maximization(EM)algorithm.The EM algorithm is an iterative method suitable for models with a latent variable,for example,when we have mixture or competing risk models.A simulation study is then conducted to examine the consistency and efficiency of the estimators and compare them.The simulation study shows that the EM approach provides a better estimation of the parameters.Finally,the proposed model is fitted to a reliability engineering data set along with some alternatives.The Akaike information criterion(AIC),Kolmogorov-Smirnov(K-S),Cramer-von Mises(CVM),and Anderson Darling(AD)statistics are used to compare the considered models.展开更多
In this article,a new generalization of the inverse Lindley distribution is introduced based on Marshall-Olkin family of distributions.We call the new distribution,the generalized Marshall-Olkin inverse Lindley distri...In this article,a new generalization of the inverse Lindley distribution is introduced based on Marshall-Olkin family of distributions.We call the new distribution,the generalized Marshall-Olkin inverse Lindley distribution which offers more flexibility for modeling lifetime data.The new distribution includes the inverse Lindley and the Marshall-Olkin inverse Lindley as special distributions.Essential properties of the generalized Marshall-Olkin inverse Lindley distribution are discussed and investigated including,quantile function,ordinary moments,incomplete moments,moments of residual and stochastic ordering.Maximum likelihood method of estimation is considered under complete,Type-I censoring and Type-II censoring.Maximum likelihood estimators as well as approximate confidence intervals of the population parameters are discussed.A comprehensive simulation study is done to assess the performance of estimates based on their biases and mean square errors.The notability of the generalized Marshall-Olkin inverse Lindley model is clarified by means of two real data sets.The results showed the fact that the generalized Marshall-Olkin inverse Lindley model can produce better fits than power Lindley,extended Lindley,alpha power transmuted Lindley,alpha power extended exponential and Lindley distributions.展开更多
Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,f...Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,for example,time to failure of a computer system.The computation of these moments is sometimes very tedious and hence some algorithms are required.One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments.Generalized order statistics pro-vides several models of ordered data as a special case.The moments of general-ized order statistics also provide moments of order statistics and record values as a special case.In this research,the recurrence relations for single,product,inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution.These relations will be helpful for obtained moments of gen-eralized order statistics from Lindley–Weibull distribution recursively.Special cases of the recurrence relations will also be obtained.Some characterizations of the distribution will also be obtained by using moments of generalized order statistics.These relations for moments and characterizations can be used in differ-ent areas of computer sciences where data is arranged in increasing order.展开更多
文摘In this paper, we introduce a class of Lindley and Weibull distributions (LW) that are useful for modeling lifetime data with a comprehensive mathematical treatment. The new class of generated distributions includes some well-known distributions, such as exponential, gamma, Weibull, Lindley, inverse gamma, inverse Weibull, inverse Lindley, and others. We provide closed-form expressions for the density, cumulative distribution, survival function, hazard rate function, moments, moments generating function, quantile, and stochastic orderings. Moreover, we discuss maximum likelihood estimation and the algorithm for computing the parameters estimates. Some sub models are discussed as an illustration with real data sets to show the flexibility of this class.
文摘In this paper, a two-parameter Lindley distribution, of which the one parameter Lindley distribution (LD) is a particular case, for modeling waiting and survival times data has been introduced. Its moments, failure rate function, mean residual life function, and stochastic orderings have been discussed. It is found that the expressions for failure rate function mean residual life function and stochastic orderings of the two-parameter LD shows flexibility over one-parameter LD and exponential distribution. The maximum likelihood method and the method of moments have been discussed for estimating its parameters. The distribution has been fitted to some data-sets relating to waiting times and survival times to test its goodness of fit to which earlier the one parameter LD has been fitted by others and it is found that to almost all these data-sets the two parameter LD distribution provides closer fits than those by the one parameter LD.
文摘In this paper, we introduce a new extension of the power Lindley distribution, called the exponentiated generalized power Lindley distribution. Several mathematical properties of the new model such as the shapes of the density and hazard rate functions, the quantile function, moments, mean deviations, Bonferroni and Lorenz curves and order statistics are derived. Moreover, we discuss the parameter estimation of the new distribution using the maximum likelihood and diagonally weighted least squares methods. A simulation study is performed to evaluate the estimators. We use two real data sets to illustrate the applicability of the new model. Empirical findings show that the proposed model provides better fits than some other well-known extensions of Lindley distributions.
文摘We proposed </span><span style="font-family:Verdana;">“</span><span style="font-family:Verdana;">a new extension of three</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">parametric distribution” called the inverse power two-parameter weighted Lindley (IPWL) distribution capable of modeling a upside-down bathtub hazard rate function. This distribution is studied to get basic structural properties such as reliability measures, moments, inverse moments and its related measures. Simulation studies </span><span style="font-family:Verdana;">are </span><span style="font-family:Verdana;">done to present the performance and behavior of maximum likelihood estimates of the IPWL distribution parameters. Finally, we perform goodness of fit measures and test statistics using a real data set to show the performance of the new distribution.
基金supported by Researchers Supporting Project Number(RSP-2021/392),King Saud University,Riyadh,Saudi Arabia.
文摘An important property that any lifetime model should satisfy is scale invariance.In this paper,a new scale-invariant quasi-inverse Lindley(QIL)model is presented and studied.Its basic properties,including moments,quantiles,skewness,kurtosis,and Lorenz curve,have been investigated.In addition,the well-known dynamic reliability measures,such as failure rate(FR),reversed failure rate(RFR),mean residual life(MRL),mean inactivity time(MIT),quantile residual life(QRL),and quantile inactivity time(QIT)are discussed.The FR function considers the decreasing or upside-down bathtub-shaped,and the MRL and median residual lifetime may have a bathtub-shaped form.The parameters of the model are estimated by applying the maximum likelihood method and the expectation-maximization(EM)algorithm.The EM algorithm is an iterative method suitable for models with a latent variable,for example,when we have mixture or competing risk models.A simulation study is then conducted to examine the consistency and efficiency of the estimators and compare them.The simulation study shows that the EM approach provides a better estimation of the parameters.Finally,the proposed model is fitted to a reliability engineering data set along with some alternatives.The Akaike information criterion(AIC),Kolmogorov-Smirnov(K-S),Cramer-von Mises(CVM),and Anderson Darling(AD)statistics are used to compare the considered models.
基金This project was funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,under grant No.(DF-279-150-1441).The authors,therefore,gratefully acknowledge DSR technical and financial support.
文摘In this article,a new generalization of the inverse Lindley distribution is introduced based on Marshall-Olkin family of distributions.We call the new distribution,the generalized Marshall-Olkin inverse Lindley distribution which offers more flexibility for modeling lifetime data.The new distribution includes the inverse Lindley and the Marshall-Olkin inverse Lindley as special distributions.Essential properties of the generalized Marshall-Olkin inverse Lindley distribution are discussed and investigated including,quantile function,ordinary moments,incomplete moments,moments of residual and stochastic ordering.Maximum likelihood method of estimation is considered under complete,Type-I censoring and Type-II censoring.Maximum likelihood estimators as well as approximate confidence intervals of the population parameters are discussed.A comprehensive simulation study is done to assess the performance of estimates based on their biases and mean square errors.The notability of the generalized Marshall-Olkin inverse Lindley model is clarified by means of two real data sets.The results showed the fact that the generalized Marshall-Olkin inverse Lindley model can produce better fits than power Lindley,extended Lindley,alpha power transmuted Lindley,alpha power extended exponential and Lindley distributions.
基金The work was funded by the University of Jeddah,Saudi Arabia under Grant Number UJ–02–093–DR.The authors,therefore,acknowledge with thanks the University for technical and financial support.
文摘Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,for example,time to failure of a computer system.The computation of these moments is sometimes very tedious and hence some algorithms are required.One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments.Generalized order statistics pro-vides several models of ordered data as a special case.The moments of general-ized order statistics also provide moments of order statistics and record values as a special case.In this research,the recurrence relations for single,product,inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution.These relations will be helpful for obtained moments of gen-eralized order statistics from Lindley–Weibull distribution recursively.Special cases of the recurrence relations will also be obtained.Some characterizations of the distribution will also be obtained by using moments of generalized order statistics.These relations for moments and characterizations can be used in differ-ent areas of computer sciences where data is arranged in increasing order.
