Measurement of the tau lepton lifetime

The mean lifetime of the tau lepton is measured in a sample of 25700 tau pairs collected in 1992 with the ALEPH detector at LEP. A new analysis of the 1-1 topology events is introduced. In this analysis, the dependence of the impact parameter sum distribution on the daughter track momenta is taken into account, yielding improved precision compared to other impact parameter sum methods. Three other analyses of the one- and three-prong tau decays are updated with increased statistics. The measured lifetime is 293.5+/-3.1+/-1.7 fs. Including previous (1989-1991) ALEPH measurements, the combined tau lifetime is 293.7+/-2.7+/-1.6 fs

A new generator for proposing flexible lifetime distributions and its properties

In this paper, we develop a generator to propose new continuous lifetime distributions. Thanks to a simple transformation involving one additional parameter, every existing lifetime distribution can be rendered more flexible with our construction. We derive stochastic properties of our models, and explain how to estimate their parameters by means of maximum likelihood for complete and censored data, where we focus, in particular, on Type-II, Type-I and random censoring. A Monte Carlo simulation study reveals that the estimators are consistent. To emphasize the suitability of the proposed generator in practice, the two-parameter Frechet distribution is taken as baseline distribution. Three real life applications are carried out to check the suitability of our new approach, and it is shown that our extension of the Frechet distribution outperforms existing extensions available in the literature

(R2027) A New Class of Pareto Distribution: Estimation and its Applications

The classical Pareto distribution is a positively skewed and right heavy-tailed lifetime distribution having a lot many applications in various fields of science and social science. In this work, via logarithmic trans-formed method, a new three parameter lifetime distribution, an extension of classical Pareto distribution is generated. The different structural properties of the new distribution are studied. The model parameters are estimated by the method of maximum likelihood and Bayesian procedure. When all the three parameters of the distribution are unknown, the Bayes estimators cannot be obtained in a closed form and hence, the Lindley’s approximation under squared error loss function is used to compute the Bayes estimators. A Monte Carlo simulation study is also conducted to compare the performance of these estimators using mean square error. The application of the new distribution for modelling earthquake insurance and reliability data are illustrated using two real data sets

A Three Parameter Generalized Lindley Distribution: Properties and Application

In this paper, we introduced a new class of lifetime distribution and considered the mathematical properties of one of the sub models called a three parameter generalized Lindley distribution (TPGLD). The new class of distributions generalizes some of the Lindley family of distribution such as the power Lindley distribution, the Sushila distribution, the Lindley-Pareto distribution, the Lindley-half logistic distribution and the classical Lindley distribution. An application of the TPGLD to two real lifetime data sets reveals its superiority over the exponentiated power Lindley distribution, the exponentiated Lindley geometric distribution, the power Lindley distribution, the Lindley-exponential distribution and the classical one parameter Lindley distribution in modeling the lifetime data sets under study

Improved measurement of the lifetime of the τ lepton

A new measurement of the τ lifetime is presented. It uses data collected with the Opal detector during 1994, which almost doubles the size of the Opal τ sample. Two statistically independent techniques are used: an impact parameter analysis of one-prong decay tracks and a fit to the decay length distribution of three-prong decays. The lifetime obtained from the 1994 data by combining the results of these methods is τ(τ) = 289.7 ± 2.5 (stat)± 1.5 (sys) fs. When combined with the previous Opal τ lifetime measurement the improved τ lifetime is τ(τ) = 289.2 ± 1.7 (stat.) ± 1.2 (sys.) fs

Inverted Beta Lindley Distribution

In this paper, a three-parameter continuous distribution, namely, Inverted Beta-Lindley (IBL) distribution is proposed and studied. The new model turns out to be quite flexible for analyzing positive data and has various shapes of density and hazard rate functions. Several statistical properties associated with this distribution are derived. Moreover, point estimation via method of moments and maximum likelihood method are studied and the observed information matrix is derived. An application of the new model to real data shows that it can give consistently a better fit than other important lifetime models

The Poisson-Lomax Distribution

In this paper we propose a new three-parameter lifetime distribution with upside-down bathtub shaped failure rate. The distribution is a compound distribution of the zero-truncated Poisson and the Lomax distributions (PLD). The density function, shape of the hazard rate function, a general expansion for moments, the density of the rth order statistic, and the mean and median deviations of the PLD are derived and studied in detail. The maximum likelihood estimators of the unknown parameters are obtained. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance-covariance matrix. Finally, a real data set is analyzed to show the potential of the new proposed distribution

The Odd Log-Logistic Gompertz Lifetime Distribution: Properties and Applications

In this paper, we introduce a new three-parameter generalized version of the Gompertz model called the odd log-logistic Gompertz (OLLGo) distribution. It includes some well-known lifetime distributions such as Gompertz (Go) and odd log-logistic exponential (OLLE) as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the kth order moment, moment generating function and the quantile measure are provided. We discuss maximum likeli- hood estimation of the OLLGo parameters as well as three other estimation methods from one observed sample. The flexibility and usefulness of the new distribution is illustrated by means of application to a real data set