Technical Reports, Statistics

Permanent URI for this collection

https://hdl.handle.net/10919/46731

Browse

Browsing Technical Reports, Statistics by Author "Hong,Yili"

Now showing 1 - 2 of 2
  • Thumbnail Image
    On Computing the Distribution Function for the Sum of Independent and Non-identical Random Indicators
    Hong,Yili (Virginia Tech, 2011-04-05)
    The Poisson binomial distribution is the distribution of the sum of independent and non-identical random indicators. Each indicator follows a Bernoulli distribution with individual success probability. When all success probabilities are equal, the Poisson binomial distribution is a binomial distribution. The Poisson binomial distribution has many applications in different areas such as reliability, survival analysis, survey sampling, econometrics, etc. The computing of the cumulative distribution function (cdf) of the Poisson binomial distribution, however, is not straightforward. Approximation methods such as the Poisson approximation and normal approximations have been used in literature. Recursive formulae also have been used to compute the cdf in some areas. In this paper, we present a simple derivation for an exact formula with a closed-form expression for the cdf of the Poisson binomial distribution. The derivation uses the discrete Fourier transform of the characteristic function of the distribution. We develop an algorithm for efficient implementation of the exact formula. Numerical studies were conducted to study the accuracy of the developed algorithm and the accuracy of approximation methods. We also studied the computational efficiency of different methods. The paper is concluded with a discussion on the use of different methods in practice and some suggestions for practitioners.
  • Thumbnail Image
    Statistical Methods for Degradation Data with Dynamic Covariates Information and an Application to Outdoor Weathering Data
    Hong,Yili; Duan, Yuanyuan; Meeker, William Q.; Stnaley, Deborah L.; Gu, Xiahohong (Virginia Tech, 2012-10-09)
    Degradation data provide a useful resource for obtaining reliability information for some highly reliable products and systems. In addition to product/system degradation measurements, it is common nowadays to dynamically record product/system usage as well as other life-affecting environmental variables such as load, amount of use, temperature, and humidity. We refer to these variables as dynamic covariate information. In this paper, we introduce a class of models for analyzing degradation data with dynamic covariate information. We use a general path model with individual random effects to describe degradation paths and a vector time series model to describe the covariate process. Shape restricted splines are used to estimate the effects of dynamic covariates on the degradation process. The unknown parameters in the degradation data model and the covariate process model are estimated by using maximum likelihood. We also describe algorithms for computing an estimate of the lifetime distribution induced by the proposed degradation path model. The proposed methods are illustrated with an application for predicting the life of an organic coating in a complicated dynamic environment (i.e., changing UV spectrum and intensity, temperature, and humidity).