Wan-Kai Pang

On interval estimation of the coefficient of variation for the three-parameter Weibull, lognormal and gamma distribution: A simulation-based approach

The coefficient of variation (CV) of a population is defined as the ratio of the population standard deviation to the population mean. It is regarded as a measure of stability or uncertainty, and can indicate the relative dispersion of data in the population to the population mean. CV is a dimensionless measure of scatter or dispersion and is readily interpretable, as opposed to other commonly used measures such as standard deviation, mean absolute deviation or error factor, which are only interpretable for the lognormal distribution. CV is often estimated by the ratio of the sample standard deviation to the sample mean, called the sample CV. Even for the normal distribution, the exact distribution of the sample CV is difficult to obtain, and hence it is difficult to draw inferences regarding the population CV in the frequentist frame. Different methods of estimating the sample standard deviation as well as the sample mean result in different shapes of the sampling distribution of the sample CV, from which inferences about the population CV can be made. In this paper we propose a simulation-based Bayesian approach to tackle this problem. A set of real data is used to generate the sampling distribution of the CV under the assumption that the data follow the three-parameter Gamma distribution. A probability interval is then constructed. The method also applies easily to lognormal and Weibull distributions.

Estimation of Wind Speed Distribution Using Markov Chain Monte Carlo Techniques

The Weibull distribution is the most commonly used statistical distribution for describing wind speed data. Maximum likelihood has traditionally been the main method of estimation for Weibull parameters. In this paper, Markov chain Monte Carlo techniques are used to carry out a Bayesian estimation procedure using wind speed data obtained from the Observatory of Hong Kong. The method is extremely flexible. Inference for any quantity of interest is routinely available, and it can be adapted easily when data are truncated.

Objective comparisons of the optimal portfolios corresponding to different utility functions

This paper considers the effects of some frequently used utility functions in portfolio selection by comparing the optimal investment outcomes corresponding to these utility functions. Assets are assumed to form a complete market of the Black-Scholes type. Under consideration are four frequently used utility functions: the power, logarithm, exponential and quadratic utility functions. To make objective comparisons, the optimal terminal wealths are derived by integration representation. The optimal strategies which yield optimal values are obtained by the integration representation of a Brownian martingale. The explicit strategy for the quadratic utility function is new. The strategies for other utility functions such as the power and the logarithm utility functions obtained this way coincide with known results obtained from Mertons dynamic programming approach.

Behavioral Estimation of Mathematical Programming Objective Function Coefficients

We propose a parameter estimation method based on what we call the minimum decisional regret principle. We focus on mathematical programming models with objective functions that depend linearly on costs or other parameters. The approach is illustrated for cost estimation in production planning using linear programming models. The method uses past planning data to estimate costs that are otherwise difficult to estimate. We define a monetary measure of distance between observed plans and optimal ones, called decisional regret. The proposed estimation algorithm finds parameter values for which the associated optimal plans are as near as possible to the observed ones on average. Such techniques may be called behavioral estimation because they are based on the observed planning or decision-making behavior of managers or firms. Two numerical illustrations are given. A supporting hyperplane algorithm is used to solve the estimation model. A method is proposed for obtaining range estimates of the parameters when multiple alternative estimates exist. We also propose a new validation approach for this estimation principle, which we call the target-mode agreement criterion.

A simulation-based approach to the study of coefficient of variation of dividend yields

Existing empirical studies of dividend yields and dividend policies either make no assumption or the normal distribution of the dividend yields data. The statistical results will be biased because they cannot reflect the finite support set property of dividend yields which can only range from 0 to 1. We posit that the assumption that dividend yields follow a beta distribution is more appropriate. The coefficient of variation (CV) is used to measure the stability of dividend yields. If we assume dividend yields follow a normal distribution, then the maximum likelihood estimate for coefficient of variation is given by . This only gives us a point estimate, which cannot depict the full picture of the sampling distribution of the coefficient of variation. A simulation-based approach is adopted to estimate CV under the beta distribution. This approach will give us a point estimate as well as the empirical sampling distribution of CV. With this approach, we study the stability of dividend yields of the Hang Seng index and its sub-indexes of the Hong Kong stock market and compare the results with the traditional approach.

A simulation based approach to the parameter estimation for the three-parameter gamma distribution☆

Abstract The gamma distribution is one of the commonly used statistical distribution in reliability. While maximum likelihood has traditionally been the main method for estimation of gamma parameters, Hirose has proposed a continuation method to parameter estimation for the three-parameter gamma distribution. In this paper, we propose to apply Markov chain Monte Carlo techniques to carry out a Bayesian estimation procedure using Hirose’s simulated data as well as two real data sets. The method is indeed flexible and inference for any quantity of interest is readily available.

On a proper way to select population failure distribution and a stochastic optimization method in parameter estimation

It is widely accepted that the Weibull distribution plays an important role in reliability applications. The reliability of a product or a system is the probability that the product or the system will still function for a specified time period when operating under some confined conditions. Parameter estimation for the three parameter Weibull distribution has been studied by many researchers in the past. Maximum likelihood has traditionally been the main method of estimation for Weibull parameters along with other recently proposed hybrids of optimization methods. In this paper, we use a stochastic optimization method called the Markov Chain Monte Carlo (MCMC) to carry out the estimation. The method is extremely flexible and inference for any quantity of interest is easily obtained.

A Further VDR-type Density Representation Based on the Box-muller Method

In recent papers a concept called vertical density representation was derived from the well-known Box-Muller method for generating normally distributed deviates. In this paper we show that this method may be regarded as one particular solution to a density composition equation. We then derive a second such solution. We also illustrate an extension of the method to certain normal-like densities.

Non-uniform random variate generation by the vertical strip method

Abstract In this paper, a method called the vertical strip (VS) method is proposed for generating non-uniform random variates with a given density. It can be considered as an improvement of the grid method as the VS method avoids setting up a directory to store information on big rectangles. Unlike the horizontal strip method that is based on the Riemann integral, the VS method is based on the Lebesgue integral and can be applied to unbounded densities or densities with infinite support. Applications of the VS method for generating random variates, which follow the exponential distribution and normal density, are also given.

Borrowing cost reduction by interest rate swaps--an option pricing analysis

Abstract Interest rate swaps generally involve two firms with different credit ratings. A quality spread differential (QSD) is observed to exist at different maturities for firm debts with different credit ratings. The quality spread differential allows two firms with different credit ratings to decrease their borrowing costs through interest rate swaps by utilising their comparative advantage in borrowing in different markets. The credit ratings of firms are determined by credit risk factors such as leverage and volatility of earnings asset value. This paper investigates the effect of the leverage and the volatility on the behaviour of risk premia between firm debts with different credit ratings by using the contingent claim analysis. Our results show that the quality spread differential can be explained by the differences in leverage and volatility. Thus two firms with different leverage and volatility of earnings asset value will benefit from interest rate swaps. However, it is found that the duration within which the QSD exists is limited by the values of the leverage and the volatility of two firms. In conclusion, this paper shows that interest rate swaps can help the firms to lower borrowing costs without necessarily relying on the arbitrage argument asserted by existing literature.