On Inequalities and Selection of Experiments for Length 
Biased Distributions

Oluyede, Broderick O.

doi:10.1017/s0269964899132030

Cited by 38 publications

(24 citation statements)

References 8 publications

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“…While demonstrating the above notation and relations, these examples are also required for the proof of Proposition 1. We shall use VF's terminology and compute for each of the four examples the appropriate functionals related to the basis NEF F = F 1 and the three EDM's: G (see (6) and (7)),G (see (10) and (11)) and f α (G) (see (14) and (15)). The binomial and negative binomial NEF's are displayed in Table 1, the Poisson and gamma in Table 2.…”

Section: Preliminaries a Problem Formulation And A Characterizationmentioning

confidence: 99%

“…Numerous works on various aspects of length-biased sampling are available in the literature. For recent publications see Oluyede (1999Oluyede ( ,2000Oluyede ( ,2003, van Es, Klaassen and Oudshoorn (2000), El Barmi (2002), and the references cited therein. Characterization results on invariant length-biased distributions in the Pearson family can be found in Sankaran and Unnikrishnan (1993).…”

Section: Introductionmentioning

confidence: 99%

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A note on exponential dispersion models which are invariant under length-biased sampling

Bar‐Lev

Schouten

2004

Statistics & Probability Letters

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A note on exponential dispersion models which are invariant under length-biased sampling Bar-Lev, S.K.; van der Duyn Schouten, F.A. Publication date: 2003 Link to publication Citation for published version (APA):Bar-Lev, S. K., & van der Duyn Schouten, F. A. (2003). A note on exponential dispersion models which are invariant under length-biased sampling. (CentER Discussion Paper; Vol. 2003-84). Tilburg: Operations research. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract Length-biased sampling situations may occur in clinical trials, reliability, queueing models, survival analysis and population studies where a proper sampling frame is absent. In such situations items are sampled at rate proportional to their "length" so that larger values of the quantity being measured are sampled with higher probabilities. More specifically, if f (x) is a p.d.f. presenting a parent population composed of nonnegative valued items then the sample is practically drawn from a distribution with p.d.f. g(x) = xf (x)/E(X) describing the lengthbiased population. In this case the distribution associated with g is termed a length-biased distribution. In this note we present a unified approach for characterizing exponential dispersion models which are invariant, up to translations, under various types of length-biased sampling. The approach is rather simple as it reduces such invariance problems into differential equations in terms of the derivatives of the associated variance functions.

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Section: Preliminaries a Problem Formulation And A Characterizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A note on exponential dispersion models which are invariant under length-biased sampling

Bar‐Lev

Schouten

2004

Statistics & Probability Letters

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“…Patil and Rao (1978) presented some useful concepts. We like to mention here the works of Gupta and Keating (1985), Gupta and Kirmani (1990), Oluyede (1999) and references therein. There are two types of weighted distributions: length biased and size biased distributions.…”

Section: Introductionmentioning

confidence: 99%

Weighted Distributions: A Brief Review, Perspective and Characterizations

Saghir¹,

Hamedani²,

Tazeem³

et al. 2017

IJSP

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The weighted distributions are widely used in many fields such as medicine, ecology and reliability, to name a few, for the development of proper statistical models. Weighted distributions are milestone for efficient modeling of statistical data and prediction when the standard distributions are not appropriate. A good deal of studies related to the weight distributions have been published in the literature. In this article, a brief review of these distributions is carried out. Implications of the differing weight models for future research as well as some possible strategies are discussed. Finally, characterizations of these distributions based on a simple relationship between two truncated moments are presented.

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“…Weighted distributions are employed mainly in research associated with reliability, bio-medicine, meta-analysis, econometrics, survival analysis, renewal processes, physics, ecology and branching processes which are found in Patil and Rao (1978), Gupta and Kirmani (1990), Gupta and Keating (1985), Oluyede (1999), Patil and Ord (1976) and Zelen and Feinleib (1969). A weighted form of Rayleigh distribution has been published by Reshi et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Vol. 16, No. 2 (Full Issue)

2017

J. Mod. App. Stat. Meth.

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EDITORIAL ASSISTANCEJMASM (ISSN 1538−9472, http://digitalcommons.wayne.edu/jmasm) is an independent, open access electronic journal, published biannually in May and November by JMASM Inc. (PO Box 48023, Oak Park, MI, 48237) in collaboration with the Wayne State University Library System. JMASM seeks to publish (1) new statistical tests or procedures, or the comparison of existing statistical tests or procedures, using computer-intensive Monte Carlo, bootstrap, jackknife, or resampling methods, (2) the study of nonparametric, robust, permutation, exact, and approximate randomization methods, and (3) applications of computer programming, preferably in Fortran (all other programming environments are welcome), related to statistical algorithms, pseudo-random number generators, simulation techniques, and self-contained executable code to carry out new or interesting statistical methods.Journal correspondence (other than manuscript submissions) and requests for advertising may be forwarded to ea@jmasm.com. See back matter for instructions for authors. IntroductionComputer simulation studies represent an important tool for investigating statistical procedures difficult or impossible to study using mathematical theory or real data. Descriptors of these studies vary (e.g., statistical experiment, Monte Carlo simulation, computer experiment), but the examples of Hoaglin and Andrews (1975) and Hauck and Anderson (1984) are followed here with use of the term simulation studies. Extensive descriptions of simulation studies can be found in Lewis and Orav (1989) and Santner, Williams, and Notz (2003). In the behavioral sciences simulation studies have been used to study a wide array of statistical methods (e.g., Cribbie, Fiksenbaum, & Wilcox, 2012; Depaoli, 2012; Enders, Baraldi, & Cham, 2014; Hu & Bentler, 1999; Tomarken & Serlin, 1986). The general goal of these studies is to provide evidence of the behavior of statistical methods under a variety of data conditions that improves statistical practice and informs future statistical research. The goal here is to encourage methodological researchers to treat these studies as statistical sampling EXPERIMENTAL DESIGN AND DATA ANALYSIS IN SIMULATION 4 experiments subject to established principles of experimental design and data analysis.An underappreciated facet of simulation studies in statistics is their role in enhancing the reproducibility of scientific findings. The importance of reproducibility has gained momentum in numerous scientific arenas because of growing evidence that many findings cannot be replicated (Stodden, 2015). Concerns over reproducibility and the role of statistics were captured in Statistics and science: A report of the London workshop on the future of the statistical sciences (2014) which noted: "The reproducibility problem goes far beyond statistics, of course, because it involves the entire reward structure of the scientific enterprise. Nevertheless, statistics is a very important ingredient in both the problem and the remedy." (p. 27) Simulati...

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On Inequalities and Selection of Experiments for Length Biased Distributions

Cited by 38 publications

References 8 publications

A note on exponential dispersion models which are invariant under length-biased sampling

A note on exponential dispersion models which are invariant under length-biased sampling

Weighted Distributions: A Brief Review, Perspective and Characterizations

Vol. 16, No. 2 (Full Issue)

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