1,721,065 research outputs found
bivgeom
Full text linkImplements Roy's bivariate geometric model (Roy (1993) ): joint probability mass function, distribution function, survival function, random generation, parameter estimation, and more
A comparison of methods for estimating parameters of the type I discrete Weibull distribution
No full textThe type I discrete Weibull distribution can be used in reliability problems for modeling discrete failure data, such as the number of shocks, cycles, or runs a component or structure can overcome before failing. This paper refines and compares some existing methods for estimating its parameters and proposes and evaluates approximate confidence intervals for large samples. A Monte Carlo simulation study was performed in order to assess the statistical performance of the methods for different parameter combinations and sample sizes and then give some indication for their mindful use. Examples are considered as a practical application of the proposed procedures. A software implementation of the model is provided as a contributed package in the RR programming environment, which reveals a useful and friendly tool for the researcher who has to handle discrete Weibull data
Discrete analogues of continuous bivariate probability distributions
No full textIn many real-world applications, the random variables modeling the phenomena of interest are continuous in nature, but their observed values are actually discrete and hence it is reasonable and convenient to choose an appropriate multivariate discrete distribution generated from the underlying continuous model preserving one or more important features.
In this work, two methods are discussed for deriving a bivariate discrete probability distribution from a continuous one by retaining some specific features of the original stochastic model, namely 1) the joint density function, or 2) the joint survival function. These methods can be regarded as the bivariate extension of two popular methods used for deriving a univariate discrete distribution from a continuous one; they can be also used as viable alternatives to extant techniques of construction of bivariate discrete random
variables. Examples of applications are presented, which involve two types of bivariate exponential distributions and a bivariate Pareto distribution, in order to illustrate how the procedures work and show that some bivariate discrete distributions that were recently proposed in the literature can be actually regarded as discrete counterparts of well-known continuous models. A numerical study is presented in order to illustrate how the procedures are practically implemented and to present inferential aspects. A real
dataset is eventually fitted using two discrete analogues of a bivariate exponential distribution
Inference on reliability of stress-strength models for poisson data
Full text linkResearchers in reliability engineering regularly encounter variables that are discrete in nature, such as the number of events (e.g., failures) occurring in a certain spatial or temporal interval. The methods for analyzing and interpreting such data are often based on asymptotic theory, so that when the sample size is not large, their accuracy is suspect. This paper discusses statistical inference for the reliability of stress-strength models when stress and strength are independent Poisson random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator are here presented and empirically compared in terms of their mean square error; recalling the delta method, confidence intervals based on these point estimators are proposed, and their reliance is investigated through a simulation study, which assesses their performance in terms of coverage rate and average length under several scenarios and for various sample sizes. The study indicates that the two estimators possess similar properties, and the accuracy of these estimators is still satisfactory even when the sample size is small. An application to an engineering experiment is also provided to elucidate the use of the proposed method
A discrete analogue of the half-logistic distribution based on the mimicking of the probability density function
No full textA count distribution obtained as a discrete version of the continuous half-logistic distribution is introduced. It is derived by assigning to each non-negative integer value a probability proportional to the corresponding value of the density function of the parent model. Statistical properties of this new distribution, in particular related to its shape, moments, and reliability concepts, are described. Parameter estimation, which can be carried out resorting to different methods including maximum likelihood, is discussed and a numerical comparison between the methods, based on Monte Carlo simulations, is presented. The applicability of the proposed distribution is proved on a real dataset, which has been already fitted by other well-established count distributions. In order to increase the flexibility of this counting model, a generalization is finally suggested, which is obtained by adding a shape parameter to the continuous one-parameter half-logistic and then applying the same discretization technique, based on the mimicking of the density function
An alternative discrete skew Laplace distribution
No full textIn this paper, an alternative discrete skew Laplace distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The distribution’s properties are explored and it is compared to a Laplace distribution on integers recently proposed in the literature. The issues related to the sample estimation of its parameters are discussed, with a particular focus on the maximum likelihood method and large-sample confidence intervals based on Fisher’s information matrix; a modified version of the method of moments is presented along with the method of proportion, which is particularly suitable for such a discrete model. Two hypothesis tests are suggested. A Monte Carlo simulation study is carried out to assess the statistical properties of these inferential techniques. Applications of the proposed model to real data are given as well
Comparing interval estimators for reliability in a dependent set-up
No full textIn this paper some procedures for building confidence intervals for the reliability in stress-strength models are discussed and empirically compared. The particular case of a bivariate normal setup is considered. The confidence intervals suggested are obtained employing approximations or asymptotic properties of maximum likelihood estimators. The coverage and the precision of these
intervals are empirically checked through a simulation study. An application to real paired data is also provided
Least-squares and minimum chi-square estimation in a discrete Weibull model
No full textIn this work, we investigate the properties of least-squares and minimum chi-square methods for the point estimation of the two parameters characterizing a discrete Weibull distribution. The first method, inflected into three variants, is based on the empirical cumulative distribution function and provides a closed analytical expression for each estimate. The second method is based on the minimization of the well-known chi-square statistic, which provides a numerical solution. A Monte Carlo simulation study empirically assesses the performance of the methods; two applications on real data show how the inferential techniques practically work
DiscreteWeibull: Discrete Weibull Distributions (Type 1 and 3)
No full textProbability mass function, distribution function, quantile function, random generation and parameter estimation for the type I and III discrete Weibull distribution
A proposal for modeling and simulating correlated discrete Weibull variables
Full text linkResearchers in applied sciences are often concerned with multivariate random variables. In particular, multivariate discrete data often arise in many fields (statistical quality control, biostatistics, failure and reliability analysis, etc.) and modeling such data is a relevant task, as well as simulating correlated discrete data satisfying some specific constraints. Here we consider the discrete Weibull distribution as an alternative to the popular Poisson random variable and propose a procedure for simulating correlated discrete Weibull random variables, with marginal distributions and correlation matrix assigned by the user. The procedure indeed relies upon the Gaussian copula model and an iterative algorithm for recovering the proper correlation matrix for the copula ensuring the desired correlation matrix on the discrete margins. A simulation study is presented, which empirically assesses the performance of the procedure in terms of accuracy and computational burden, also in relation to the necessary (but temporary) truncation of the support of the discrete Weibull random variable. Inferential issues for the proposed model are also discussed and are eventually applied to a dataset taken from the literature, which shows that the proposed multivariate model can satisfactorily fit real-life correlated counts even better than the most popular or recent existing ones
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