Author

# Pedro Jodrá

Bio: Pedro Jodrá is an academic researcher from University of Zaragoza. The author has contributed to research in topics: Lambert W function & Poisson distribution. The author has an hindex of 9, co-authored 24 publications receiving 332 citations.

##### Papers

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TL;DR: These procedures are based on the fact that the quantile functions of these probability distributions can be expressed in closed form in terms of the Lambert W function, and so the extreme order statistics from the above distributions can also be computer generated in a straightforward manner.

Abstract: We provide procedures to generate random variables with Lindley distribution, and also with Poisson-Lindley or zero-truncated Poisson-Lindley distribution, as simple alternatives to the existing algorithms. Our procedures are based on the fact that the quantile functions of these probability distributions can be expressed in closed form in terms of the Lambert W function. As a consequence, the extreme order statistics from the above distributions can also be computer generated in a straightforward manner.

84 citations

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TL;DR: In this article, exact closed-form expressions for the Kolmogorov and the total variation distances between Poisson, binomial, and negative binomial distributions with different parameters are given.

Abstract: We give exact closed-form expressions for the Kolmogorov and the total variation distances between Poisson, binomial, and negative binomial distributions with different parameters. In the Poisson case, such expressions are related with the Lambert
function.

72 citations

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TL;DR: A linear algorithm is presented for solving the traveling repairman problem when the underlying graph is a path, improving the Θ(N2) time and space complexity of the previously best algorithm for this problem.

Abstract: Given a finite set of N nodes and the time required for traveling among nodes, in the traveling repairman problem, we seek a route that minimizes the sums of the delays for reaching each node. In this note, we present a linear algorithm for solving the traveling repairman problem when the underlying graph is a path, improving the Θ(N2) time and space complexity of the previously best algorithm for this problem. We also provide a linear algorithm for solving the walk problem with deadlines (WPD) on paths. © 2002 Wiley Periodicals, Inc.

42 citations

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TL;DR: The Muth distribution is a continuous random variable introduced in the context of reliability theory as mentioned in this paper, and some mathematical properties of the model are derived, including analytical expressions for the moment generating function, moments, mode, quantile function and moments of the order statistics.

Abstract: The Muth distribution is a continuous random variable introduced in the context of reliability theory. In this paper, some mathematical properties of the model are derived, including analytical expressions for the moment generating function, moments, mode, quantile function and moments of the order statistics. In this regard, the generalized integro-exponential function, the Lambert W function and the golden ratio arise in a natural way. The parameter estimation of the model is performed by the methods of maximum likelihood, least squares, weighted least squares and moments, which are compared via a Monte Carlo simulation study. A natural extension of the model is considered as well as an application to a real data set.

27 citations

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TL;DR: A closed-form expression in terms of the Lambert W function for the quantile function of the Gompertz-Makeham distribution is given, helpful to generate random samples drawn from this probability distribution by means of the inverse transform method.

Abstract: In this note, we give a closed-form expression in terms of the Lambert W function for the quantile function of the Gompertz-Makeham distribution. This probability distribution has frequently been used to describe human mortality and to establish actuarial tables. The analytical expression provided for the quantile function is helpful to generate random samples drawn from the Gompertz-Makeham distribution by means of the inverse transform method.

25 citations

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1,196 citations

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TL;DR: A new two-parameter power Lindley distribution is introduced and its properties are discussed, which include the shapes of the density and hazard rate functions, the moments, skewness and kurtosis measures, the quantile function, and the limiting distributions of order statistics.

Abstract: A new two-parameter power Lindley distribution is introduced and its properties are discussed. These include the shapes of the density and hazard rate functions, the moments, skewness and kurtosis measures, the quantile function, and the limiting distributions of order statistics. Maximum likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Three algorithms are proposed for generating random data from the proposed distribution. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators of the parameters as well as the coverage probability and the width of the confidence interval for each parameter. An application of the model to a real data set is presented finally and compared with the fit attained by some other well-known two-parameter distributions.

269 citations

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01 Nov 2011TL;DR: In this paper, a new distribution is proposed for modeling lifetime data, which has better hazard rate properties than the gamma, lognormal and the Weibull distributions, including a real data example is discussed to illustrate its applicability.

Abstract: A new distribution is proposed for modeling lifetime data. It has better hazard rate properties than the gamma, lognormal and the Weibull distributions. A comprehensive account of the mathematical properties of the new distribution including estimation and simulation issues is presented. A real data example is discussed to illustrate its applicability.

207 citations

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145 citations