By N. Balakrishnan, Enrique Castillo, Jose-Maria Sarabia Alegria

During this quantity, a number of distinctive and energetic researchers will spotlight the various fresh advancements in statistical distribution thought, order facts and their houses, and a few inferential equipment linked to them. the amount is classed into varied components in response to the focal point of the articles. functions of the distributions and inferential approaches into survival research, reliability, qc, and environmental difficulties might be highlighted. This complete reference paintings will serve the statistical and utilized arithmetic groups in addition to practitioners, researchers and grad scholars in utilized likelihood and data, reliability engineering, and biostatistics.

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In reliability theory and survival analysis the hazard rate (or failure rate) function ru{t) = fu{t)/Fu{t) provides a useful characterization of the random variable U (when it exists), and represents the instantaneous rate of failure at time t given survival up to time t. We begin our list of some basic stochastic orders with the well-known and classical usual stochastic order. 2 If the hazard rate function of U is less than that of V at all points t {ru{t) < ry{t)), then we say that U exceeds V in the hazard r a t e o r d e r and write U >hr V, U is greater than V in the likelihood ratio o r d e r (and we write U>irV ) if fu{t)/fv{t) T *• Generally speaking, the usual stochastic order, the hazard rate order, and the likelihood ratio order are probably the most frequently used stochastic orders, although the last two are perhaps not of much practical use when comparing sums of Bernoulli random variables.

Villasenor), Statistics & Probability Letters, 33, 35-39. 134. Specification of bivariate distributions. , S. Kotz, C. B. Read, and D. L. Banks), pp. 61-63, John Wiley & Sons, New York. 135. Gumbel records and related characterizations, (with J. A. , N. L. Johnson and N. Balakrishnan), pp. 441-453, John Wiley & Sons, New York. 136. Characterizations involving conditional specification. Journal of Statistical Planning and Inference, 63, 117-131. 1998 137. The use of conditionally conjugate priors in the study of ratios of gamma scale parameters (with E.

88. Bivariate distributions with conditionals in prescribed exponential families (with D. Strauss), Journal of the Royal Statistical Association, Series B, 53, 365-375. Publications xxxi 89. Lorenz ordering of exponential order statistics (with H. N. Nagaraja), Statistics & Probability Letters^ 11, 485-490. 90. On some properties of bivariate weighted distributions (with H. N. Nagaraja), Communications in Statistics—Theory and Methods, 20, 18531860. 91. Pseudo-UkeHhood estimation: Some examples (withD.