Simons, Gordon
Overview
Works:  43 works in 74 publications in 1 language and 148 library holdings 

Roles:  Author 
Classifications:  QA276, 
Publication Timeline
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Most widely held works by
Gordon Simons
A largedimensional iid property for nearest neighbor counts in Poisson processes by
YiChing Yao(
Book
)
2 editions published in 1994 in English and held by 13 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 13 WorldCat member libraries worldwide
Precision calculation of distributions for trimmed sums by
Sándor Csörgő(
Book
)
2 editions published in 1994 in English and held by 13 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 13 WorldCat member libraries worldwide
A strong law of large numbers for trimmed sums, with applications to generalized St. Petersburg games by
Sándor Csörgő(
Book
)
2 editions published in 1994 in English and held by 13 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 13 WorldCat member libraries worldwide
Asymptotic sine laws arising from alternating random permutations and sequences by
Gordon Simons(
Book
)
2 editions published in 1993 in English and held by 12 WorldCat member libraries worldwide
2 editions published in 1993 in English and held by 12 WorldCat member libraries worldwide
A three color problem by
Gordon Simons(
Book
)
2 editions published in 1991 in English and held by 12 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 12 WorldCat member libraries worldwide
On a problem of ammunition rationing by
Lawrence A Shepp(
Book
)
2 editions published in 1990 in English and held by 11 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 11 WorldCat member libraries worldwide
Estimating distortion consistently : an algebraic approach by
Gordon Simons(
Book
)
2 editions published in 1989 in English and held by 10 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 10 WorldCat member libraries worldwide
Some results on the bomber problem by
Gordon Simons(
Book
)
3 editions published in 1989 in English and held by 9 WorldCat member libraries worldwide
3 editions published in 1989 in English and held by 9 WorldCat member libraries worldwide
On [alpha]symmetric multivariate distributions by
Stamatis Cambanis(
Book
)
2 editions published in 1981 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1981 in English and held by 3 WorldCat member libraries worldwide
Sequential estimators and the CramérRao lower bound by
Gordon Simons(
Book
)
3 editions published in 1979 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1979 in English and held by 3 WorldCat member libraries worldwide
Probability and expectation inequalities by
Stamatis Cambanis(
Book
)
3 editions published in 1980 in English and held by 3 WorldCat member libraries worldwide
This paper introduces a mathematical framework within which a wide variety of known and new inequalities can be viewed from a common perspective. Probability and expectation inequalities of the following types are considered: (a) P(Z epsilon A)> or = P(Z' epsilon A) for some class of sets A, (b) Ek(Z)> or = Ek(Z') for some class of functions k, and (c) El (Z)> or = Ek(Z') for some class of of pairs of functions l and k
3 editions published in 1980 in English and held by 3 WorldCat member libraries worldwide
This paper introduces a mathematical framework within which a wide variety of known and new inequalities can be viewed from a common perspective. Probability and expectation inequalities of the following types are considered: (a) P(Z epsilon A)> or = P(Z' epsilon A) for some class of sets A, (b) Ek(Z)> or = Ek(Z') for some class of functions k, and (c) El (Z)> or = Ek(Z') for some class of of pairs of functions l and k
Research on Statistical Procedures in Reliability Engineering by
Ralph A Evans(
Book
)
1 edition published in 1975 in English and held by 2 WorldCat member libraries worldwide
The 'time saved on life tests' by using extra items and not waiting until all items fail has been calculated for the exponential, Powerfunction, and Pareto distributions. The expected values for time ratios are calculated in 3 different ways and the results are quite different. For example, for 7 items tested to the first 3 failures, as compared to 3 items tested to 3 failures, the ratio of expected times is 0.28, whereas the expected ratio is 0.37 (with dependence) and is 0.44 (with independence)
1 edition published in 1975 in English and held by 2 WorldCat member libraries worldwide
The 'time saved on life tests' by using extra items and not waiting until all items fail has been calculated for the exponential, Powerfunction, and Pareto distributions. The expected values for time ratios are calculated in 3 different ways and the results are quite different. For example, for 7 items tested to the first 3 failures, as compared to 3 items tested to 3 failures, the ratio of expected times is 0.28, whereas the expected ratio is 0.37 (with dependence) and is 0.44 (with independence)
Existence of optimal stopping rules for rewards related to Sn̳/n by
Gordon Simons(
Book
)
3 editions published in 1967 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1967 in English and held by 2 WorldCat member libraries worldwide
The minimax risk for clinical trials by John Bather(
Book
)
1 edition published in 1984 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1984 in English and held by 2 WorldCat member libraries worldwide
A Weak Invariance Principle with Applications to Domains of Attraction by
Gordon Simons(
Book
)
2 editions published in 1975 in English and held by 2 WorldCat member libraries worldwide
An elementary probabilistic argument is given which establishes a 'weak invariance principle' which in turn implies the sufficiency of the classical assumptions associated with the weak convergence of normed sums to stable laws. The argument, which uses quantile functions (the inverses of distribution functions), exploits the fact that two random variables X = F sup( 1)(U) and Y = G sup( 1)(U) are, in a useful sense, close together when F and G are, in a certain sense, close together. Here U denotes a uniform variable on (0,1). Byproducts of the research are two alternative characterizations for a random variable being in the domain of partial attraction to a normal law and some results concerning the study of domains of partial attraction
2 editions published in 1975 in English and held by 2 WorldCat member libraries worldwide
An elementary probabilistic argument is given which establishes a 'weak invariance principle' which in turn implies the sufficiency of the classical assumptions associated with the weak convergence of normed sums to stable laws. The argument, which uses quantile functions (the inverses of distribution functions), exploits the fact that two random variables X = F sup( 1)(U) and Y = G sup( 1)(U) are, in a useful sense, close together when F and G are, in a certain sense, close together. Here U denotes a uniform variable on (0,1). Byproducts of the research are two alternative characterizations for a random variable being in the domain of partial attraction to a normal law and some results concerning the study of domains of partial attraction
Optimality within the class of sequential probability ratio tests by
Gordon Simons(
Book
)
1 edition published in 1974 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1974 in English and held by 2 WorldCat member libraries worldwide
On the cost of not knowing the variance when making a fixedwidth confidence interval of the mean by
Gordon Simons(
Book
)
2 editions published in 1967 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1967 in English and held by 2 WorldCat member libraries worldwide
A sequential estimation of tall probabilities in exponential distributions with a prescribed proportional closeness by
Gordon Simons(
Book
)
3 editions published in 1967 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1967 in English and held by 2 WorldCat member libraries worldwide
Generalized cumulative distribution functions: I. The linear case with applications to nonparametric statistics by
Gordon Simons(
Book
)
2 editions published in 1972 in English and held by 2 WorldCat member libraries worldwide
The author investigates the behavior of (univariate) cumulative distribution functions which are defined on an abstract linearly ordered space. Special emphasis is given to the study of a class of linearly ordered spaces which J.H.B. Kemperman introduced into the subject of monparametric tolerance regions. Distribution functions on such spaces can be decomposed. Considerable attention is given to applications. In particular, it is shown how a number of nonparametric statistical procedures can be extended to include situations of multivariate and time dependent data. (Author)
2 editions published in 1972 in English and held by 2 WorldCat member libraries worldwide
The author investigates the behavior of (univariate) cumulative distribution functions which are defined on an abstract linearly ordered space. Special emphasis is given to the study of a class of linearly ordered spaces which J.H.B. Kemperman introduced into the subject of monparametric tolerance regions. Distribution functions on such spaces can be decomposed. Considerable attention is given to applications. In particular, it is shown how a number of nonparametric statistical procedures can be extended to include situations of multivariate and time dependent data. (Author)
On characterization of the gamma distribution by
W. J Hall(
Book
)
2 editions published in 1968 in English and held by 1 WorldCat member library worldwide
Let X sub 1, X sub 2 ... be a sequence of i.i.d. random variables and S sub n = summation, j = 1 to j = n, of X sub j. If X sub 1 has a gamma distribution, (Z sub n is identically equal to S(subscript n, superscript r)/E(S subscript n, superscript r)); n = or> 1) is a reverse martingale sequence for any positive r. These reverse martingales find applications in sequential analysis. In this paper the converse is proved for any integer r> 1, and this provides a characterization of the gamma distribution; in fact, it is sufficient that the reverse martingale sequence have finite length r. Another characterization is also proved, extending the case r = 2 to nonidentically distributed r.v.'s. (Author)
2 editions published in 1968 in English and held by 1 WorldCat member library worldwide
Let X sub 1, X sub 2 ... be a sequence of i.i.d. random variables and S sub n = summation, j = 1 to j = n, of X sub j. If X sub 1 has a gamma distribution, (Z sub n is identically equal to S(subscript n, superscript r)/E(S subscript n, superscript r)); n = or> 1) is a reverse martingale sequence for any positive r. These reverse martingales find applications in sequential analysis. In this paper the converse is proved for any integer r> 1, and this provides a characterization of the gamma distribution; in fact, it is sufficient that the reverse martingale sequence have finite length r. Another characterization is also proved, extending the case r = 2 to nonidentically distributed r.v.'s. (Author)
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Related Identities
 University of North Carolina (System) Institute of Statistics
 University of North Carolina at Chapel Hill Department of Statistics
 Yao, YiChing Author
 Csörgő, Sándor 19472008 Author
 Stanford University Department of Statistics
 Shepp, Lawrence A. 1936 Author
 University of North Carolina at Chapel Hill Department of Biostatistics
 Cambanis, Stamatis Author
 National Science Foundation (U.S.)
 Feder, Paul (Paul Ira) Author
Associated Subjects
Chebyshev approximation Convergence Distribution (Probability theory) DrugsTesting Elliptic functions Entropy (Information theory) Ergodic theory Estimation theory Mappings (Mathematics) Martingales (Mathematics) Mathematical statistics Mathematical statisticsAsymptotic theory Multivariate analysis Optimal stopping (Mathematical statistics) Permutations Poisson processes Probabilities Sequential analysis Topology Transformations (Mathematics) Trigonometrical functions