Graybill, Franklin A.
Overview
Works:  38 works in 292 publications in 10 languages and 6,220 library holdings 

Roles:  Author, Honoree, Other 
Classifications:  HA29, 311 
Publication Timeline
.
Most widely held works by
Franklin A Graybill
Introduction to the theory of statistics by
Alexander M Mood(
Book
)
111 editions published between 1950 and 2013 in 7 languages and held by 2,131 WorldCat member libraries worldwide
Probability; Random variables, distribution functions, and expectation; Special parametric families of univariate distributions; Joint and conditional distributions, stochastic independence, more expectation; Distributions of functions of random variables; Sampling and sampling distributions; Parametric interval estimation; Tests of hypotheses; Linear models; Nonparametric method
111 editions published between 1950 and 2013 in 7 languages and held by 2,131 WorldCat member libraries worldwide
Probability; Random variables, distribution functions, and expectation; Special parametric families of univariate distributions; Joint and conditional distributions, stochastic independence, more expectation; Distributions of functions of random variables; Sampling and sampling distributions; Parametric interval estimation; Tests of hypotheses; Linear models; Nonparametric method
Introduction to matrices with applications in statistics by
Franklin A Graybill(
Book
)
30 editions published between 1968 and 2002 in English and held by 973 WorldCat member libraries worldwide
30 editions published between 1968 and 2002 in English and held by 973 WorldCat member libraries worldwide
An introduction to linear statistical models by
Franklin A Graybill(
Book
)
36 editions published between 1961 and 1976 in English and German and held by 756 WorldCat member libraries worldwide
36 editions published between 1961 and 1976 in English and German and held by 756 WorldCat member libraries worldwide
An introduction to statistical models in geology by
William Christian Krumbein(
Book
)
15 editions published between 1965 and 1972 in English and held by 642 WorldCat member libraries worldwide
15 editions published between 1965 and 1972 in English and held by 642 WorldCat member libraries worldwide
Theory and application of the linear model by
Franklin A Graybill(
Book
)
22 editions published between 1976 and 2000 in 3 languages and held by 500 WorldCat member libraries worldwide
"In THEORY AND APPLICATION OF THE LINEAR MODEL, Franklin A. Graybill integrates the linear statistical model within the context of analysis of variance, correlation and regression, and design of experiments. With topics motivated by real situations, it is a time tested, authoritative resource for experimenters, statistical consultants, and students."BN overview
22 editions published between 1976 and 2000 in 3 languages and held by 500 WorldCat member libraries worldwide
"In THEORY AND APPLICATION OF THE LINEAR MODEL, Franklin A. Graybill integrates the linear statistical model within the context of analysis of variance, correlation and regression, and design of experiments. With topics motivated by real situations, it is a time tested, authoritative resource for experimenters, statistical consultants, and students."BN overview
Regression analysis : concepts and applications by
Franklin A Graybill(
Book
)
10 editions published between 1993 and 1994 in English and Undetermined and held by 215 WorldCat member libraries worldwide
10 editions published between 1993 and 1994 in English and Undetermined and held by 215 WorldCat member libraries worldwide
Probability and statistics : essays in honor of Franklin A. Graybill(
Book
)
7 editions published in 1988 in English and held by 170 WorldCat member libraries worldwide
7 editions published in 1988 in English and held by 170 WorldCat member libraries worldwide
Applied statistics : a first course in inference by
Franklin A Graybill(
Book
)
7 editions published in 1998 in English and held by 121 WorldCat member libraries worldwide
7 editions published in 1998 in English and held by 121 WorldCat member libraries worldwide
SAS laboratory manual to accompany Regression analysis : concepts and applications by
Franklin A Graybill(
Book
)
2 editions published in 1994 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 8 WorldCat member libraries worldwide
Student solutions manual for regression analysis : concepts and applications by
Franklin A Graybill(
Book
)
2 editions published in 1994 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 6 WorldCat member libraries worldwide
An introduction to linear statistical models by
Franklin A Graybill(
)
1 edition published in 1961 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1961 in English and held by 4 WorldCat member libraries worldwide
Statističeskie modeli v geologii by
William C Krumbein(
Book
)
2 editions published in 1969 in Russian and held by 3 WorldCat member libraries worldwide
2 editions published in 1969 in Russian and held by 3 WorldCat member libraries worldwide
Tōkeigaku nyūmon(
Book
)
5 editions published between 1969 and 1978 in Japanese and held by 2 WorldCat member libraries worldwide
5 editions published between 1969 and 1978 in Japanese and held by 2 WorldCat member libraries worldwide
İstatistik teorisine giriş by
Alexander M Mood(
Book
)
2 editions published in 1973 in Turkish and held by 2 WorldCat member libraries worldwide
2 editions published in 1973 in Turkish and held by 2 WorldCat member libraries worldwide
Confidence Intervals on a Ratio of Variances in the TwoFactor Nested Components of Variance Model by
Franklin A Graybill(
Book
)
3 editions published in 1980 in English and held by 2 WorldCat member libraries worldwide
Consider the twofactor nested components of variance model Y sub ijk = mu + A sub i + B sub ij + C sub ijk, where Var(A sub i) = sigma squared sub A Var(B sub ij) = sigmasquared sub B, Var(C sub ijk) = sigmasquared sub C. Confidence intervals are derived for sigmasquared sub A/sigmasquared sub C, sigmasquared sub A (sigmasquared sub A + sigmasquared sub C) and sigmasquared sub C/(sigmasquared sub A + sigmasquared sub C). (Author)
3 editions published in 1980 in English and held by 2 WorldCat member libraries worldwide
Consider the twofactor nested components of variance model Y sub ijk = mu + A sub i + B sub ij + C sub ijk, where Var(A sub i) = sigma squared sub A Var(B sub ij) = sigmasquared sub B, Var(C sub ijk) = sigmasquared sub C. Confidence intervals are derived for sigmasquared sub A/sigmasquared sub C, sigmasquared sub A (sigmasquared sub A + sigmasquared sub C) and sigmasquared sub C/(sigmasquared sub A + sigmasquared sub C). (Author)
On quadratic estimates of variance components ... by
Franklin A Graybill(
)
1 edition published in 1952 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1952 in English and held by 2 WorldCat member libraries worldwide
Confidence Intervals on Nonnegative Linear Combinations of Variances by
Franklin A Graybill(
Book
)
2 editions published between 1979 and 1980 in English and held by 2 WorldCat member libraries worldwide
Smith (1936) suggested a method that can be used for setting confidence limits on linear combinations of variances. This method was studied and expanded by Satterthwaite (1941, 1946) and has become known as Satterthwaite's procedure. The procedure has been widely used for the past 40 years. In this paper a new procedure is proposed for this problem that is better than Satterthwaite's procedure and very easy to compute from existing tables. (Author)
2 editions published between 1979 and 1980 in English and held by 2 WorldCat member libraries worldwide
Smith (1936) suggested a method that can be used for setting confidence limits on linear combinations of variances. This method was studied and expanded by Satterthwaite (1941, 1946) and has become known as Satterthwaite's procedure. The procedure has been widely used for the past 40 years. In this paper a new procedure is proposed for this problem that is better than Satterthwaite's procedure and very easy to compute from existing tables. (Author)
On quadratic estimates of variance components by
Franklin A Graybill(
)
1 edition published in 1952 in English and held by 1 WorldCat member library worldwide
Quadratic estimates of variance components for various linear models were investigated;For the general balanced nested classification with no specific distributions assumed, it was shown that the quadratic estimate which was unbiased and which had minimum variance was given by the analysis of variance method of estimating the variance components;For the one fold classification with unequal numbers the model is yij=m+ai+bij where E ai2 = sigma a2; E bij2 = sigma 2;The best quadratic unbiased estimate of sigmaa2 depends on sigma2 and sigmaa2. Under the above model with the additional assumptions E ai 4 = 3 sigmaa4 and E bij 4 = 3 sigma4 the quadratic estimation of sigma a2 was investigated. Two methods of estimation were given, and a method of determining a lower bound on the efficiency of each method was given if w = sigmaa2/sigma2 is known. It is believed in most cases when w > .01, that one of these two methods will give an efficiency above 80 percent;For the general balanced cross classification with normality assumptions it was shown that the best quadratic unbiased estimate of the variance components is given by the analysis of variance method of estimating variance components. It was also shown that the best quadratic unbiased estimate of any linear combination of variance components is given by the same linear combination of the best quadratic unbiased estimates of the individual variance components
1 edition published in 1952 in English and held by 1 WorldCat member library worldwide
Quadratic estimates of variance components for various linear models were investigated;For the general balanced nested classification with no specific distributions assumed, it was shown that the quadratic estimate which was unbiased and which had minimum variance was given by the analysis of variance method of estimating the variance components;For the one fold classification with unequal numbers the model is yij=m+ai+bij where E ai2 = sigma a2; E bij2 = sigma 2;The best quadratic unbiased estimate of sigmaa2 depends on sigma2 and sigmaa2. Under the above model with the additional assumptions E ai 4 = 3 sigmaa4 and E bij 4 = 3 sigma4 the quadratic estimation of sigma a2 was investigated. Two methods of estimation were given, and a method of determining a lower bound on the efficiency of each method was given if w = sigmaa2/sigma2 is known. It is believed in most cases when w > .01, that one of these two methods will give an efficiency above 80 percent;For the general balanced cross classification with normality assumptions it was shown that the best quadratic unbiased estimate of the variance components is given by the analysis of variance method of estimating variance components. It was also shown that the best quadratic unbiased estimate of any linear combination of variance components is given by the same linear combination of the best quadratic unbiased estimates of the individual variance components
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Associated Subjects
Analysis of variance Canada Confidence intervals Experimental design GeologyMathematical models GeologyStatistical methods Graybill, Franklin A Linear models (Statistics) Mathematical statistics Mathematics Matrices Multivariate analysis Probabilities Regression analysis SAS (Computer file) Scientists Statistics United States