Inferential Methods for Bivariate Logistic Model

Abstract

<p>There are several methods available for estimating the parameters of bivariate logistic model. In this report, we compare the method of Maximum Likelihood (MLM), weighted least squares cdf method (WLS), elemental percentile method (EPM) and Castillo's least square method (CLS) for estimating the parameters λ, δ, σ, τ, of bivariate logistic model. We perform Monte Carlo simulation to compare the MLM, WLS and CLS on the basis of mean squared errors (MSE) and bias of the estimators δ and τ by keeping λ = 0 and σ = 1 fixed. It has been found that no method is uniformly better than the others, but MLM and CLS perform better than the others in terms of MSE. We compared MLM and CLS on the basis of average confidence lengths for δ and τ. It has been found that MLM produces shorter confidence intervals than the CLS. In the CLS method, three different weights, β = 0.5, 0.9, 1, have been considered and comparative results for this method are also presented.</p> <p>We applied four methods of estimation to the UK pig production data (1967- '78) as the bivariate logistic distribution has been found to be a good fit to this data (Castillo, Sarabia and Hadi 1997). We compared all four methods on the basis of MSE, bias and lengths of confidence intervals for the parameters λ, 𝛿, σ, τ using bootstrap resampling technique. Again, MLM and CLS are found to be performing better than the other two methods, which agrees with the results obtained using Monte Carlo simulation.</p> <p>CLS has been found to be advantageous than MLM for small sample size (e.g., n < 25) and especially when the scale parameters are very small.</p>