Selection from Logistic populations

Assume k ( k ≥ 2) independent populations π₁, π₂μ_k are given. The associated independent random variables X_i,( i = 1,2,… k ) are Logistically distributed with unknown means μ₁, μ₂, μ_k and equal variances. The goal is to select that population which has the largest mean. The procedure is to select that population which yielded the maximal sample value. Let μ₍₁₎≤μ₍₂₎≤…≤μ_(k) denote the ordered means. The probability of correct selection has been determined for the Least Favourable Configuration μ₍₁₎=μ₍₂₎==μ_{(k – 1)}=μ_(k)–δ where δ > 0. An exact formula for the probability of correct selection is given.     

Large deviation principles and loglog laws for observation processes

Let ( X_n, n ≥ 1) be an i.i.d. sequence of positive random variables with distribution function H . Let φ _H := {(n, X_n ), n ≥ 1) be the associated observation process. We view φ h as a measure on E := [0, ∞) ∞ (0, φ] where φ_H (A) is the number of points of φ _H which lie in A . A family ( V_s, s> 0) of transformations is defined on E in such a way that for suitable H the distributions of ( V_sφ_H, S > 0) satisfy a large deviation principle and that a related Strassen-type law of the iterated logarithm also holds. Some consequent large deviation principles and loglog laws are derived for extreme values. Similar results are proved for φ _H replaced by certain planar Poisson processes.     

Fourier inversion and the Hausdorff distance

This paper continues research done by F.H. Ruymgaart and the author. For a function f on R ^d we consider its Fourier transform F f and the functions f_M (M>0) derived from F f by the formula f_M(x) =( F( ε_M · F f ))(− x );, where the ε_M are suitable integrable functions tending to 1 pointwise as M →∞. It was shown earlier that, relative to a metric d _H , analogous to the Hausdorff distance between closed sets, one has d _H (f_M, f) = O( M ^−½) for all f in a certain class. We now show that, for such f , the estimate O( M ^−½) is optimal if and only if f has a discontinuity point.     

Approximation for the cumulative and inverse gamma distribution

The gamma distribution function can be expressed in terms of the Normal distribution and density functions with sufficient accuracy for most practical purposes.
The distribution function for the density x^Λ-1e^-x/μ/μ^ΛΓ(A) on 0 -R(Λ){(1 + 1/1 2Λ) φ(z) + 11 -z/4Λ^1/2+2(z²+ 2)/45Λ] φ(z) /3 Λ^1/2} where φ(z)≅1/[1 +_e^{-2z(√2/π+z2 /28)}] and φ(z) = e^{-z2 /2}/√2π are the Normal distribution and density functions, y is the appropriate root of y-y²/6+y³/36-y⁴/270= In (x/Λμ), z= Λ^1/2 y, and R( Λ) is the remainder term in Stirling's approximation for In Γ(Λ).     

The HR/IR Teaching Conference

This article summarizes and analyzes the 1996 Innovative Teaching in Human Resources and Industrial Relations (HR/IR) Conference. It deals with the (1) origins, content, and format of the conference; (2) key trends, ideas, and themes that emerged from the conference; and (3) implications from the analysis for the next HR/IR teaching conference (scheduled for June 1999). Special attention is paid to the different disciplinary approaches to teaching HR/IR, newer nontraditional methods for teaching HR/IR, and practitioner influence on HR/IR teaching and research. © 1999 John Wiley & Sons, Inc.     

Inequalities relating maximal moments to other measures of dispersion

Let X , X ₁, ..., X_k be i.i.d. random variables, and for k ∈ N let D_k ( X ) = E ( X ₁ V ... V X _{k +1}) − EX be the k th centralized maximal moment. A sharp lower bound is given for D ₁( X ) in terms of the Lévy concentration Q_l ( X ) = sup _{x ∈ R} P ( X ∈[ x , x + l ]). This inequality, which is analogous to P. Levy's concentration-variance inequality, illustrates the fact that maximal moments are a gauge of how much spread out the underlying distribution is. It is also shown that the centralized maximal moments are increased under convolution.     

Some remarks concerning the quotient of sample median and sample range for a sample of size 2n+1 from a normal distribution

Consider an ordered sample ₍₁₎, ₍₂₎,…, _(2n+1) of size 2 n +1 from the normal distribution with parameters μ and . We then have with probability one
₍₁₎ < ₍₂₎ < … < (2 n +1).
The random variable
_n =_(n+1)/_(2n+1)-(1)
that can be described as the quotient of the sample median and the sample range, provides us with an estimate for μ/, that is easy to calculate. To calculate the distribution of h _n is quite a different matter***. The distribution function of h₁, and the density of h₂ are given in section 1. Our results seem hardly promising for general h_n. In section 2 it is shown that h_n is asymptotically normal.
In the sequel we suppose μ= 0 and = 1, i.e. we consider only the "central" distribution. Note that h_n can be used as a test statistic replacing Student's t. In that case the central h_n is all that is needed.     

The “Iron Law of Paternalism” in Employee Grievances and Arbitration? A Comparison of Disciplinary and Nondisciplinary Cases

In the criminology literature, the iron law of paternalism suggests that women receive less serious sanctions in the judicial system. This examination of three years of grievance outcomes (n= 1216) and arbitration outcomes (n= 1146) tests this iron law in the context of organizational disciplinary and dispute resolutions. These data, across several levels of outcomes (win, lose, compromise), controlling for the severity of grievances (disciplinary/nondisciplinary) and arbitrations (termination/nontermination) provide no support for the paternalistic thesis. Moreover, we find no support for the paternalistic thesis with regard to either the incidence or length of suspensions as a function of gender.     

A model of diffusion and implementation: An exploratory study of managerial innovation in Colombia

The focus of this paper is characterized by (1) an examination of the factors related to the “anticipation” of potential innovations in any organizational setting and (2) the identification of strategies for the diffusion and implementation of operations research/management science (OR/MS) techniques in a particular developing region. Based on the methodology used in studying change (innovation) in health care systems, a managerial innovation model incorporating four main components [the executive, the organization, the task environment of the organization and change agent(s), including the OR/MS manager and outside consultants] is developed and examined in terms of data obtained from top executives and other managers in forty industrial firms in Cali, Colombia. In the model developed the process of innovation is decomposed into the levels of; (a) attitudes and motivations of the executive, (b) “readiness” to take action, (c) action characteristics, (d) triggering cues and (e) actions taken and evaluation (feedback loop). The model was found useful for providing predictions indicating areas to which intervention and “marketing” of OR/MS strategies should be devoted. Overall, the study provides a base for comparative and longitudinal studies.     

First-Order Integer-Valued Autoregressive (INAR (1)) Process: Distributional and Regression Properties

Some properties of a first-order integer-valued autoregressive process (INAR)) are investigated. The approach begins with discussing the self-decomposability and unimodality of the 1-dimensional marginals of the process {X_n} generated according to the scheme X_n=α° X _n-i +e_n, where α° X _n-1 denotes a sum of X_{n - 1}, independent 0 - 1 random variables Y^(n-1), independent of X _n-1 with Pr -( y ^{(n - 1)}= 1) = 1 - Pr ( y ^(n-i)= 0) =α. The distribution of the innovation process ( e _n) is obtained when the marginal distribution of the process ( X _n) is geometric. Regression behavior of the INAR(1) process shows that the linear regression property in the backward direction is true only for the Poisson INAR(1) process.     

An alternate development of conditioning

Abstract  The "classical" development of conditioning, due to K olmogorov , does not agree with the "practical" (more intuitive, but unrigorous) way in which probabilists and statisticians actually think about conditioning. This paper describes an alternative to the classical development. It is shown that standard concepts and results can be developed, rigorously, along lines, which correspond to the "practical" approach, and so as to include the classical material as a special case. More specifically, let Xand Y be random variables (r.v.'s) from (Ω, f, P) to ( x, f_x ) and (y. f^y.), respectively. In this paper, the fundamental concept is the conditional probability P(AX = x ), a function of xε x which satisfies a "natural" defining condition. This is used to define a conditional distribution P_y/x, as a mapping x × f^y-R such that, as a function of B, P_ylx=x,(B ) is a probability measure on f^y. Then, for a numerical r.v. Y , conditional expectation E(Y/X) is defined as a mapping x → whose value at x isE(Y/X = x) = ydP_Y/x=i(y ). Basic properties of conditional probabilities, distributions, and expectations, are derived and their existence and uniqueness are discussed. Finally, for a sub-o-algebra and a numerical r.v. Y , the classical conditional expectation E(Y) is obtained as E(Y/X) with X = i , the identity mapping from (Ω, f) to (Ω).     

De omvang van de steekproef bij een enkelvoudig steekproefsysteem

Summary  (Sample size for a single sampling scheme).
The operating characteristic of a sampling scheme may be specified by the producers 1 in 20 risk point ( p ₁), at which the probability of rejecting a batch is 0.05, and the consumers 1 in 20 risk point ( p ₂) at which the probability of accepting a batch of that quality is also 0.05.
A nomogram is given (fig. 2) to determine for single sampling schemes and for given values of p₁ and p ₂ the necessary sample size ( n ) and the allowable number of defectives in the sample ( c ).
The nomogram may reversedly be used to determine the producers and consumers 1 in 20 risk points for a given single sampling scheme.
The curves in this nomogram were computed from a table of percentage points of the χ² distribution. For v > 30 Wilson and Hilferty's approximation to the χ² distribution was used.     

Estimation of a k-monotone density: characterizations, consistency and minimax lower bounds

The classes of monotone or convex (and necessarily monotone) densities on     can be viewed as special cases of the classes of k - monotone densities on     . These classes bridge the gap between the classes of monotone (1-monotone) and convex decreasing (2-monotone) densities for which asymptotic results are known, and the class of completely monotone (∞-monotone) densities on     . In this paper we consider non-parametric maximum likelihood and least squares estimators of a k -monotone density g ₀. We prove existence of the estimators and give characterizations. We also establish consistency properties, and show that the estimators are splines of degree k −1 with simple knots. We further provide asymptotic minimax risk lower bounds for estimating the derivatives     , at a fixed point x ₀ under the assumption that     .     

Kusterer or Manwaring and Wood on the High-Tech Labor Process? Analyzing the Nature of Skill,Deskilling and Managerial Control of Labor in a U.S. Medical Electronics Factory

Since Bravermans (1974) work revived interest and research in labor process theory, labor process theorists have developed differing conceptions of the nature of skill, deskilling and the managerial control of labor in the capitalist work organization. In this article, I examine two labor process theories, K. Kusterers (1978) theory of working knowledge and Manwaring and Woods (1985) theory of tacit skills, with regards to the nature of skill, deskilling and the managerial control of labor and test these two theories with respect to data obtained on unskilled and semiskilled production work at a high-tech medical electronics factory. I conclude that there is more support for Manwaring and Woods (1985) theory of tacit skills than for Kusterers (1978) theory of working knowledge for high-tech production work.     

Satisfaction,organizational commitment and future action in charity sport event volunteers

• Charity sport events (CSEs) are a key revenue source for nonprofit organizations (NPOs) with large numbers of volunteers needed for success and cost‐effectiveness. This study explored determinants of CSE volunteers' satisfaction, organizational commitment and intended future actions (CSE, other NPO activity/event volunteering, donating money). Relay for Life volunteers (N = 290) from one Australian state completed a cross‐sectional survey. Significant pathways were found from socializing/enjoyment (β = 0.17), fighting cancer (β = 0.29), financial support (β = 0.21) motives and social norm (β = 0.23) to satisfaction; 52% variance was explained. Age (β = ?0.09), survivorship (β = 0.09), region (β = 0.07), fundraising goal (β = 0.08), advocacy (β = 0.15), financial support (β = 0.25), social/enjoyment (β = 0.23) motives, social norm (β = 0.23) and satisfaction (β = 0.21) were linked with commitment; 63% variance was explained. Paths between satisfaction, commitment and intended future actions (CSE, NPO activity/event volunteering) were significant (βs = 0.17–0.43). Future targets to increase CSE volunteer satisfaction and commitment involve similar (social/enjoyment) and diverse (action‐oriented) motives, with satisfaction and commitment key contributors to future actions supporting NPOs. Copyright © 2016 John Wiley & Sons, Ltd.

     

On the asymptotically uniform distribution modulo 1 of extreme order statistics

Let (X_m)∞₁ be a sequence of independent and identically distributed random variables. We give sufficient conditions for the fractional part of rnax (X₁., X_n) to converge in distribution, as n ←∞ to a random variable with a uniform distribution on [0, 1).     

Recurrence relations for moment and conditional moment generating functions of generalized order statistics

In this paper, we obtain recurrence relations for moment and conditional moment generating functions of generalized order statistics (gos) based on random samples drawn from a population whose distribution is a member of a doubly truncated class of distributions denoted by . Members of the class are characterized in Section (2) based on recurrence relations for moment generating functions (moments) of gos. In Section (3), we shall characterize members of the class based on recurrence relations for conditional moment generating functions (conditional moments) of gos. These results are specialized to the left, right and non-truncated cases. Ordinary order statistics and ordinary record values are also obtained as special cases of the gos. Characterizations of some members of class such as the Weibull, compound Weibull, Pareto, power function (beta is a special case), Gompertz and compound Gompertz distributions are given as illustrative examples.     

A Simulation Approach to Nonparametric Empirical Bayes Analysis

We deal with general mixture of hierarchical models of the form m(x) = f_øf(x |θ) g (θ)dθ , where g(θ) and m(x) are called mixing and mixed or compound densities respectively, and θ is called the mixing parameter. The usual statistical application of these models emerges when we have data x_i, i = 1,…,n with densities f(x_i|θ_i) for given θ_i, and the θ₁ are independent with common density g(θ) . For a certain well known class of densities f(x |θ) , we present a sample-based approach to reconstruct g(θ) . We first provide theoretical results and then we use, in an empirical Bayes spirit, the first four moments of the data to estimate the first four moments of g(θ) . By using sampling techniques we proceed in a fully Bayesian fashion to obtain any posterior summaries of interest. Simulations which investigate the operating characteristics of our proposed methodology are presented. We illustrate our approach using data from mixed Poisson and mixed exponential densities.     

Continuous representations of interval orders based on induced preorders

Conditions are given for the existence of a pair of continuous real valued functions (u, v) representing an interval order on a topological space (X, ), in the sense that [xy if and only ifu(x)].I am deeply indepted to Professor Alain Chateauneuf for many valuable suggestions.     

Thin layer chromatography, a case study

This paper gives an account of the collaboration between two mathematical statisticians and a toxicologist (the second author) interested in thin layer chromatography (TLC). A TLC "system" consists of a medium through which a solvent is transported. If a solution of some (toxic) sample is applied to the medium, then the components are carried forward by the solvent over different distances. Section 1 describes the concept of a data bank which provides standard values for the degrees of migration characteristic for each of m well-studied substances in each of n systems. Sections 2–5 are mainly devoted to the construction of The "best design(s)"{ j ₁*… j _k * } of k systems from the n available ones. The attention is restricted to the situation that an unidentified sample exclusively contains one of the m substances covered by the data bank and produces the scores xj … ^xj_k in the systems j,… j _krespectively. Three different approaches to the identification problem were successively considered. Each approach leads to a class of procedures and their performances. The performance of the optimum procedure can be used to define the performance of any of the ( ⁿ_k ) designs ( j ₁… j_k }. The latter performance is maximized in order to determine { j ₁*.,., j_k* }. In practice usually data is obtained for mixtures instead of single. pure substances. Section 6 gives some tentative theory for the evaluation of such data.