Spatial prediction using bivariate exponential distribution

Abstract

In this paper, a certain bivariate exponential distribution is used for the spatial prediction. The unobserved random variable is predicted by the projection onto the space of all linear combinations of the powers, up to degree m, of the observed random variables plus the constant 1. We obtain a solution by assuming that all the bivariate distributions follow Gumbel's type III or logistic form of bivariate exponential. The method is implemented on two data sets and the results are presented. The predictions are compared with the original values through Mean Structural Similarity (MSSIM) index of Wang et al. (IEEE Trans Image Process 13(4): [600][601][602][603][604][605][606][607][608][609][610][611][612] 2004). Using the MSSIM index the proposed method is also compared with Ordinary Kriging and with Simple Kriging after normal score transform.

Uni-variate and bi-variate Inverted Exponential Teissier distribution in Bayesian and non-Bayesian framework to model stochastic dynamic variation of climate data

“…2021 ). Sometimes, using the dependence function of a Bi-variate probability distribution, a new spatial directional variogram model is introduced (Helwade and Subramanyam 2010 ) for disjunctive kriging. Many researchers also propose a mixture type of distribution to determine the threshold condition where, the head of the frequency curve is modeled by a gamma distribution, and the curve’s tail is explained by generalized Pareto distribution (Kim et al.…”

Uni-variate and Bi-variate Inverted Exponential-Teissier Distribution in Bayesian and Non-Bayesian framework to Model Stochastic Dynamic Variation of Climate data

“…For example, the behavior of daily rainfall data in two geographic locations, namely, Lazio and Sicily, located in central and south Italy, are explained using six probability distributions, Frechet, Gumbel, Pareto type-II, Weibull, and Log-normal Moccia et al (2021). Sometimes, using the dependence function of a Bi-variate probability distribution, a new spatial directional variogram model is introduced Helwade and Subramanyam (2010) for disjunctive kriging. Many researchers also propose a mixture type of distribution to determine the threshold condition where, the head of the frequency curve is modeled by a gamma distribution, and the curve's tail is explained by generalized Pareto distribution Kim et al (2019).…”