We derive analytic expressions for the biases, to O(n-1), of the maximum likelihood estimators of the parameters of the generalized Pareto distribution. Using these expressions to bias-correct the estimators is found to be extremely effective in terms of bias reduction, and can also result in a...

We derive analytic expressions for the biases, to O(n-1), of the maximum likelihood estimators of the parameters of the generalized Rayleigh distribution family. Using these expressions to bias-correct the estimators is found to be extremely effective in terms of bias reduction, and generally...

The Topp-Leone distribution is attractive for reliability studies as it has finite support and a bathtub-shaped hazard function. We compare some properties of the method of moments, maximum likelihood, and bias-adjusted maximum likelihood estimators of its shape parameter. The last of these...

We investigate the small-sample quality of the maximum likelihood estimators (MLEs) of the parameters of the zero-inflated Poisson distribution. The finite-sample biases are determined to O(n-1) using an analytic bias reduction methodology based on the work of Cox and Snell (1968) and Cordeiro...

We derive analytic expressions for the biases, to O(n-1) of the maximum likelihood estimators of the parameters of the generalized Pareto distribution. Using these expressions to bias-correct the estimators is found to be extremely effective in terms of bias reduction, and generally results in...

We derive an analytic expression for the bias, to O(n-1) of the maximum likelihood estimator of the scale parameter in the half-logistic distribution. Using this expression to bias-correct the estimator is shown to be very effective in terms of bias reduction, without adverse consequences for...

We consider the quality of the maximum likelihood estimators for the parameters of the two-parameter gamma distribution in small samples. We show that the methodology suggested by Cox and Snell (1968) can be used very easily to bias-adjust these estimators. A simulation study shows that this...

We use the stochastic volatility model as a basis for investigating the statistical properties of absolute returns as a measure of latent volatility in financial markets. Our results are compared with existing results for squared returns.

We show that the full asymptotic null distribution for Watson’s 2N U statistic, modified for discrete data, can be computed simply and exactly by standard methods. Previous approximate quantiles for the uniform multinomial case are found to be accurate. More extensive quantiles are presented...

Gold, and other precious metals, are among the oldest and most widely held commodities used as a hedge against the risk of disruptions in financial markets. The prices of such metals fluctuate substantially, introducing a risk of its own. This paper’s goal is to analyze the risk of investment...