Characterizations of geometric distribution and discrete IFR (DFR) distributions using order statistics

Let X be a discrete random variable the set of possible values (finite or infinite) of which can be arranged as an increasing sequence of real numbers a₁<a₂<a₃<…. In particular, a_i could be equal to i for all i. Let X_1n≦X_2n≦?≦X_nn denote the order statistics in a random sample of size n drawn from the distribution of X, where n is a fixed integer ≧2. Then, we show that for some arbitrary fixed k(2≦k≦n), independence of the event {X_kn=X_1n} and X_1n is equivalent to X being either degenerate or geometric. We also show that the montonicity in i of P{X_kn = X_1n | X_1n = a_i} is equivalent to X having the IFR (DFR) property. Let a_i = i and $\text{G(i) = P(X≧i), i = 1, 2, …}$. We prove that the independence of {X_2n ? X_1n ∈B} and X_1n for all i is equivalent to X being geometric, where B = {m} (B = {m,m+1,…}), provided G(i) = q^i?1, 1≦i≦m+2 (1≦i≦m+1), where 0<q<1.     

The experience of carrying out the technical responsibility system in the birth control of Peng County, Sichuan Province]

Following the establishment of the system of fixed responsibility in production in Peng County, Sichuan Province, the County's Family Planning Office and Public Health Bureau in 1980 broadened the system of technical responsibility in birth control by defining tasks and goals. The commune public health office should guide birth control technology, lower the incidence of unplanned pregnancies and the number of abortions. The number of fertile women using IUDs should be over 80%, and its failure rate should be less then 10%; the failure rate of male ligature should be less than 3%. Commune members should give 1 jiao to the public health office for expenses incurred in birth control technology. If all the goals are reached, then there would be economic rewards outside the total public support system. That is, 1 jiao is awarded for each IUD inserted, 2 jiao for male ligatures and 3 jiao for female ligatures. Infractions such as poor attitude, irresponsibility, or delaying surgery are fined from 1-20 yuan. The following situations resulted from having implemented the system of technical responsibilty for birth control: 1) medical personnel had the authority to initiate action concerning birth control technology; 2) the quality of surgery was raised, while the incidence of errors was lowered; 3) the costs of surgery were lowered; and 4) because abortions are not awarded with economic incentives, medical personnel tended to perform more preventive surgery rather than corrective surgery.     

DETERMINATION OF DOMAINS OF ATTRACTION BASED ON A SEQUENCE OF MAXIMA

Suppose that the maximum of a random sample from a distribution F(x) may be obtained in each of k equally spaced observation periods. This paper proposes a test to determine the domain of attraction of F(x), and investigates the properties when the sample size is very large and perhaps unknown and k is fixed and small. The test statistic is a function of the spacings between the order statistics based on the sequence of maxima and is suggested by reference to one studied previously when inference was based on the largest k observations of a random sample. A Monte Carlo study shows that the proposed test is more powerful than its main competitor. The test is illustrated by two examples.     

Checking adequacy of the semiparametric location shift model with censored data

The location shift model is commonly used to quantify the difference between groups in a two-arm study. Nonparametric inference procedures for the location shift parameter with censored observations have recently been extensively studied. However, the validity of these procedures depends heavily on the model assumption. In this article, a class of graphical and numerical methods are proposed for checking the adequacy of the location shift model. Our graphical procedures are much less subjective than the eye-ball method based on the standard Q-Q plot. The proposed methods are illustrated with real-life examples.     

Extrapolation designs and Φp-optimum designs for cubic regression on the q-ball

This paper continues earlier work of the authors in carrying out the program discussed in Kiefer (1975), of comparing the performance of designs under various optimality criteria. Designs for extrapolation problems are also obtained. The setting is that in which the controllable variable takes on values in the q-dimensional unit ball, and the regression is cubic. Thus, the ideas of comparison are tested for a model more complex than the quadratic models discussed previously. The E-optimum design performs well in terms of other criteria, as well as for extrapolation to larger balls. A method of simplifying the calculations to obtain approximately optimum designs, is illustrated.     

Demographic characteristics and shared values

This study investigated the extent to which person-organization values alignment is affected by demographic variables (e.g., gender, age, educational level, marital status, family status, hierarchical level, years of managerial experience, and organizational size) across a wide variety of organizations. Values alignment, using two separate measures, was directly related to positive work attitudes and this relationship was moderated by several respondent characteristics. The potential impact of organizational acculturation is proposed as minimizing the impact of demographic factors within organizations.     

The significance of the sample lead:alternative proof

This paper presents an alternative derivation of the expected value and variance of the sample lead to the one given in a previous paper. It deals with the case of random sampling from infinite population without replacement or from finite population with replacement. The derivation involves the use of the moment- and cumulant-generating functions, but is shorter and simpler than the original proofs.