Many applications from economic and financial practice lead to optimization problems depending on a probability measure. A complete knowledge of the "underlying" measure is a necessary assumption to determine an exact optimal solution and an exact optimal value. Since this condition is not...

This article presents the estimation methods of three parameters Discrete Generalized Exponential distribution. The two-parameter generalized exponential distribution was introduced by Gupta and Kundu (1999). We present the three parameters discrete Generalized Exponential distribution is the...

This paper considers the specification and performance of jackknife estimators of the autoregressive coefficient in a model with a near-unit root. The limit distributions of sub-sample estimators that are used in the construction of the jackknife estimator are derived, and the joint moment...

This paper examines the impact of the parameters of the distribution of the time at which a bank's client defaults on their obligated payments, on the Lundberg adjustment coefficient, the upper and lower bounds of the ruin probability. We study the corresponding ruin probability on the...

Abstract Some classes of lifetime distributions based on the failure rate are considered, namely new better than used failure rate (NBUFR), new better than average renewal failure rate (NBARFR) and generalized new better than average renewal failure rate (GNBARFR). Moment inequalities and moment...

Abstract Weibull distributions are popular models for quality and reliability. In this note, we investigate a distribution proposed by Bousquet et al. as an alternative to the Weibull distribution. We derive – for the first time – explicit and general expressions for the moments and the...

This paper uses the empirical characteristic function (ECF) procedure to estimate the parameters of mixtures of normal distributions. Since the characteristic function is uniformly bounded, the procedure gives estimates that are numerically stable. It is shown that, using Monte Carlo simulation,...

This paper is concerned with the application of jackknife methods as a means of bias reduction in the estimation of autoregressive models with a unit root. It is shown that the usual jackknife estimator based on non-overlapping sub-samples does not remove fully the first-order bias as intended,...

In this paper, we describe a tool to aid in proving theorems about random variables, called the moment generating function, which converts problems about probabilities and expectations into problems from calculus about function values and derivates. We show how the moment generating function...