On the performance of a new bivariate pseudo Pareto distribution with application to drought data

Quantifying uncertainty in multivariate quantile estimation of hydrometeorological extremes via copula: A comparison between bootstrapping and Markov chain Monte Carlo

“…Earlier studies have compared uncertainty estimation methods, bootstrapping and MCMC, based on the confidence interval sizes, coverage probability, point estimation bias, and combinations of these three criteria. The criterion related to confidence interval size selects the method with the smallest confidence interval, and is used mostly with pure empirical samples whose distribution parameters are unknown (Patterson, 1999; Mohsin et al ., 2012). The criterion related to coverage probability selects the method with the highest coverage probability (Magnusson et al ., 2013), or the method that generates the largest number of acceptable confidence intervals (with a coverage probability higher than a certain threshold) when tested with more than one dataset (Panagoulia et al ., 2014), and is used mostly with theoretical samples whose true distribution parameters are known.…”

“…Using theoretical distributions, they compared the quantile matching qualities and confidence intervals of the three methods and found MCMC performs best with minimal uncertainty, followed by the profile likelihood method, then bootstrapping. Mohsin et al (2012) compared bootstrapping and MCMC in estimating the parameters of a novel bivariate pseudo Pareto distribution for drought analysis. Bootstrapping and MCMC were found to perform similarly, with synthetic data as well as with real data.…”

“…Mohsin et al . (2012) compared bootstrapping and MCMC in estimating the parameters of a novel bivariate pseudo Pareto distribution for drought analysis. Bootstrapping and MCMC were found to perform similarly, with synthetic data as well as with real data.…”

“…This study is more comprehensive than most. We consider various combinations of distributions for multiple sets of observed data, as opposed to the bulk majority of previous research that compared just one or two distributions at a time (Mohsin et al ., 2012; Chen et al ., 2016). This gives us greater confidence in the generalizability of our findings, which may be of interest to researchers and practitioners alike when selecting the best method for quantifying the uncertainty of hydrometeorological extremes.…”

Extremal and additive processes generated by Pareto distributed random vectors

“…The bivariate Pareto distribution of the first kind has received widespread applications: joint distribution of drivers' injuries in road accidents [18]; modeling of clustering of sociopathy and hysteria in families [19]; outlier tests [3]; Bayesian inference [1]; modeling of the life lengths of components of a system sharing a common environment [28]; theory of queues [32]; modeling the detection of targets in a combat [55]; modeling of operational risk [37]; modeling of daily exchange rate data for four major currencies [47]; reliability evaluation for a multi-state system under stress-strength setup [11]; risk estimation [22]; drought modeling [38]; modeling of bodily injury liability closed claims [54]; statistical analyses on the tail losses of equity portfolios constructed from the stock indexes of six major global financial markets [27]; to mention just a few.…”