TY - JOUR
T1 - Statistical inference for the Weitzman overlapping coefficient in a family of distributions
AU - Montoya, José A.
AU - P., Gudelia Figueroa
AU - González-Sánchez, David
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/7/1
Y1 - 2019/7/1
N2 - © 2019 Elsevier Inc. A usual problem in applied statistics is the one related to the estimation of the common area under two distributions, which is usually estimated by means of an overlapping coefficient. Particularly, for the Weitzman overlapping coefficient, we found that it is possible to provide a general expression that facilitates making inferences on this coefficient, for many distributions. This expression depends only on two parameters which are actually functions of the parameters of the selected models, among which we can mention the exponential, Weibull, Gumbel, Fréchet and some other distributions that arise under certain transformations of an exponential random variable. The simplicity of our unifying proposal is illustrated considering three well known distributions that have been individually analyzed in statistical literature. To illustrate the performance of the likelihood confidence intervals obtained for this overlapping coefficient, under our proposal, we carried out some simulation studies that yielded adequate coverage frequencies, and just for the sake of comparison we also computed Bootstrap confidence intervals. A real data set is analyzed to exemplify our proposal.
AB - © 2019 Elsevier Inc. A usual problem in applied statistics is the one related to the estimation of the common area under two distributions, which is usually estimated by means of an overlapping coefficient. Particularly, for the Weitzman overlapping coefficient, we found that it is possible to provide a general expression that facilitates making inferences on this coefficient, for many distributions. This expression depends only on two parameters which are actually functions of the parameters of the selected models, among which we can mention the exponential, Weibull, Gumbel, Fréchet and some other distributions that arise under certain transformations of an exponential random variable. The simplicity of our unifying proposal is illustrated considering three well known distributions that have been individually analyzed in statistical literature. To illustrate the performance of the likelihood confidence intervals obtained for this overlapping coefficient, under our proposal, we carried out some simulation studies that yielded adequate coverage frequencies, and just for the sake of comparison we also computed Bootstrap confidence intervals. A real data set is analyzed to exemplify our proposal.
KW - Coverage frequency
KW - Family of likelihoods
KW - Likelihood confidence interval
KW - Overlapping parameter
KW - Reliability parameter
KW - Wilcoxon-Mann-Whitney statistic
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U2 - 10.1016/j.apm.2019.02.036
DO - 10.1016/j.apm.2019.02.036
M3 - Artículo
AN - SCOPUS:85062803520
SN - 0307-904X
VL - 71
SP - 558
EP - 568
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
ER -