S H Hou

Multiobjective second-order symmetric duality with F-convexity☆

We suggest a pair of second-order symmetric dual programs in multiobjective nonlinear programming. For these second-order symmetric dual programs, we prove the weak, strong and converse duality theorems under F-convexity conditions.

Second order symmetric duality in non-differentiable multiobjective programming with F-convexity

Abstract This paper is concerned with a pair of Mond–Weir type second order symmetric dual non-differentiable multiobjective programming problems. We establish the weak and strong duality theorems for the new pair of dual models under second order F -convexity assumptions. Several results including many recent works are obtained as special cases.

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 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.

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.

Further results on multivariate vertical density representation and an application to random vector generation

In this paper we further develop the theory of vertical density representation (VDR) in the multivariate case and provide a formula for the calculation of the conditional probability density of a random vector when its density value is given. An application to random vector generation is also given.

Performance of some boundary-seeking mode estimators on the dome bias model

Abstract Expert estimates can be systematically biased for various reasons. The dome perspective bias model provides one instance of this phenomenon. Given data with this suspected property, it is desirable to propose mode estimators which have the capability of producing consensus estimates on the boundary of the convex hull of the sample. Affine linear models are no doubt the simplest class of functions with that capability. This paper uses the maximum decisional efficiency (MDE) principle to estimate the parameters of an affine linear group value function. These estimators vary according to the sample aggregator chosen. Estimators are developed or approximated for the aggregator choices of (i) mean, (ii) minimum or Leontief, and (iii) variance. The respective performances of these estimators are assessed and compared on the dome perspective bias model using Monte Carlo simulation experiments. The estimator based on the mean performed uniformly well on a variety of simulated cases. However, those based on range and variance were not effective.