On the asymptotic distribution of Matusita's overlapping measure

Numerical Integral Approximation to Estimate Matusita Overlapping Coefficient for Normal Distributions

“…Assume that we have two independent random samples x 11 ,x 12 ,…,x 1n1 ) of size n 1 and x 21 ,x 22 ,…,x 2n2 ) of size n 2 , where the two samples are generated from N(0,1) and N(μ 2 ,σ 2 2 ),(μ 2 ,σ 2 2 )=(-0.2,1.1),(2.5,4),(3.5,1.5),(10,2.5) respectively. These selection values of μ 1 ,σ 1 2 μ 2 ,σ 2 2 are chosen to vary the exact values of ρ between 0 and 1 From each pair of distributions, 1000 samples of sizes (n 1 ,n 2 )= (24,30), (54,54),(96,180) were simulated independently from the two normal distributions N(μ 1 ,σ 1 2 ) and N(μ 2 ,σ 2 2 ) with selected parameters given in Table (1). The empirical results given in Table (1) were calculated based on one thousand replications (R=1000).…”

“…These selection values of μ 1 ,σ 1 2 μ 2 ,σ 2 2 are chosen to vary the exact values of ρ between 0 and 1 From each pair of distributions, 1000 samples of sizes (n 1 ,n 2 )= (24,30), (54,54),(96,180) were simulated independently from the two normal distributions N(μ 1 ,σ 1 2 ) and N(μ 2 ,σ 2 2 ) with selected parameters given in Table (1). The empirical results given in Table (1) were calculated based on one thousand replications (R=1000). For each estimator, we compute the relative bias (RB), relative root mean square error (RRMSE) and efficiency (EFF).…”

“…There are three well known overlapping (OVL) coefficients, namely Matusita (1955) coefficient (ρ), Morisita (1959) coefficient (λ) and Weitzman (1970) coefficient (Δ). These coefficients measure the similarity or agreement between two distributions which are very useful and used in several applications such as a measure of distinctness clusters (Sneath, 1977); reliability analysis (Dhaker et al, 2019) and the goodness of fit test for two independent distributions [1]. In this paper we interest with the Matusita coefficient ρ.…”

“…Computing the overlapping coefficient ρ between two densities gives an idea about the degree of similarity or closeness of the two phenomena that follow these densities. It should be noticed that the values of above overlapping measures is bounded by [0,1]. If the value of ρ is closed to zero, this indicates no common area between the two densities .On the other hand, if its value is close to 1, this indicates complete matching of the two densities.…”

“…The unknown parameters Ө can be estimated by any rigorous statistical point estimation methods like the method of moments or the maximum likelihood (ML) estimation method. Unlike the parametric method, the nonparametric method does not require any assumptions about the shape or the formula of the underlying statistical distributions (see for example, [1,2]). The parametric method has been considered by many authors to estimate the various OVL coefficients.…”