We introduce a new generalization of the exponentiated power Lindley distribution,called the exponentiated power Lindley power series(EPLPS)distribution.The new distribution arises on a latent complementary risks scen...We introduce a new generalization of the exponentiated power Lindley distribution,called the exponentiated power Lindley power series(EPLPS)distribution.The new distribution arises on a latent complementary risks scenario,in which the lifetime associated with a particular risk is not observable;rather,we observe only the maximum lifetime value among all risks.The distribution exhibits decreasing,increasing,unimodal and bathtub shaped hazard rate functions,depending on its parameters.Several properties of the EPLPS distribution are investigated.Moreover,we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix.Finally,applications to three real data sets show the flexibility and potentiality of the EPLPS distribution.展开更多
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
文摘We introduce a new generalization of the exponentiated power Lindley distribution,called the exponentiated power Lindley power series(EPLPS)distribution.The new distribution arises on a latent complementary risks scenario,in which the lifetime associated with a particular risk is not observable;rather,we observe only the maximum lifetime value among all risks.The distribution exhibits decreasing,increasing,unimodal and bathtub shaped hazard rate functions,depending on its parameters.Several properties of the EPLPS distribution are investigated.Moreover,we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix.Finally,applications to three real data sets show the flexibility and potentiality of the EPLPS distribution.
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.
