Darling, D. A. (Donald A.)
Overview
Works:  11 works in 18 publications in 1 language and 36 library holdings 

Roles:  Author 
Classifications:  AS36, 
Publication Timeline
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Most widely held works by
D. A Darling
A new approach to the KolmogorovSmirnov distributions by
D. A Darling(
Book
)
2 editions published in 1957 in English and held by 6 WorldCat member libraries worldwide
The present approach is based on a combination firstly of the observation that the empirical distribution function of a sample of data is merely a scaled and normalized Poisson process, and secondly of certain analytical methods which have been developed in the past few years for calculating the distribution of certain additive functionals of Markov processes. In general the methods in this paper isolate the analytical difficulties in certain functional equations whose solution may be very difficult; but it seems quite powerful in obtaining asymptotic expansions
2 editions published in 1957 in English and held by 6 WorldCat member libraries worldwide
The present approach is based on a combination firstly of the observation that the empirical distribution function of a sample of data is merely a scaled and normalized Poisson process, and secondly of certain analytical methods which have been developed in the past few years for calculating the distribution of certain additive functionals of Markov processes. In general the methods in this paper isolate the analytical difficulties in certain functional equations whose solution may be very difficult; but it seems quite powerful in obtaining asymptotic expansions
The first passage problem for a continuous Markoff process by
D. A Darling(
Book
)
2 editions published in 1953 in English and held by 6 WorldCat member libraries worldwide
The solution to the first passage problem for a strongly continuous temporally homogeneous Markoff process X(t) is given. If T = T sub ab (x) is a random variable giving the time of first passage of X (t) from the region a> X(t)> b when a> X(0) = x> b, simple methods of getting the distribution of T (at least in terms of a Laplace transform) are developed. From the distribution of T the distribution of the maximum of X(t) and the range of X(t) are deduced. These results yield, in an asymptotic form, solutions to certain statistical problems in sequential analysis, nonparametric theory of 'goodness of fit, ' optional stopping, etc. which are treated as an illustration of the theory. (Author)
2 editions published in 1953 in English and held by 6 WorldCat member libraries worldwide
The solution to the first passage problem for a strongly continuous temporally homogeneous Markoff process X(t) is given. If T = T sub ab (x) is a random variable giving the time of first passage of X (t) from the region a> X(t)> b when a> X(0) = x> b, simple methods of getting the distribution of T (at least in terms of a Laplace transform) are developed. From the distribution of T the distribution of the maximum of X(t) and the range of X(t) are deduced. These results yield, in an asymptotic form, solutions to certain statistical problems in sequential analysis, nonparametric theory of 'goodness of fit, ' optional stopping, etc. which are treated as an illustration of the theory. (Author)
A systematic approach to a class of problems in the theory of noise and other random phenomena by
A. J. F Siegert(
Book
)
2 editions published between 1955 and 1957 in English and held by 5 WorldCat member libraries worldwide
The problem of finding the probability distribution of a functional, consisting of a (multidimensional) Markoff process and a given function, appears in many forms in the theory of noise and other random phenomena. It is shown that a certain function from which this probability distri bution can be obtained is the unique solution of two integral equations. A perturbation formalism which relates the solutions of the integral equations belonging to two different functions is developed. If the transition probability density is the principal solution of two partial differential equations of the FokkerPlanckKolmogoroff type, the principal solution of two similar differential equations is the solution of the integral equations. As an example the probability distribution of the sample probability density for a stationary Markoff process is calculated. (Author)
2 editions published between 1955 and 1957 in English and held by 5 WorldCat member libraries worldwide
The problem of finding the probability distribution of a functional, consisting of a (multidimensional) Markoff process and a given function, appears in many forms in the theory of noise and other random phenomena. It is shown that a certain function from which this probability distri bution can be obtained is the unique solution of two integral equations. A perturbation formalism which relates the solutions of the integral equations belonging to two different functions is developed. If the transition probability density is the principal solution of two partial differential equations of the FokkerPlanckKolmogoroff type, the principal solution of two similar differential equations is the solution of the integral equations. As an example the probability distribution of the sample probability density for a stationary Markoff process is calculated. (Author)
On the distribution of certain functionals of Markoff processes by
D. A Darling(
Book
)
2 editions published in 1954 in English and held by 5 WorldCat member libraries worldwide
The problem of the distribution of certain functionals of a general ndimensional Markoff process X(t) is explored. Analytical methods for the study of random variables are developed. A fundamental pair of integral equations whose unique solution is the characteristic function of U(s, t) is also developed
2 editions published in 1954 in English and held by 5 WorldCat member libraries worldwide
The problem of the distribution of certain functionals of a general ndimensional Markoff process X(t) is explored. Analytical methods for the study of random variables are developed. A fundamental pair of integral equations whose unique solution is the characteristic function of U(s, t) is also developed
An inventory problem : the bankruptcy questsion by
D. A Darling(
Book
)
2 editions published in 1951 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1951 in English and held by 4 WorldCat member libraries worldwide
The survival probability problem by
D. A Darling(
Book
)
1 edition published in 1950 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1950 in English and held by 3 WorldCat member libraries worldwide
Some statistical problems connected with stochastic processes by
T. W Anderson(
Book
)
2 editions published between 1949 and 1950 in English and held by 2 WorldCat member libraries worldwide
The statistical problem treated is that of testing the hypothesis that a sample of n independent, identically distributed random variables have the common continuous distribution function F(x), specified in advance. In principle such tests will give confidence regions for the unknown distribution function, for if we have a test (based on the n observations) for every F(x) the confidence region will consist of those F(x) for which the corresponding hypotheses are not rejected. (Author)
2 editions published between 1949 and 1950 in English and held by 2 WorldCat member libraries worldwide
The statistical problem treated is that of testing the hypothesis that a sample of n independent, identically distributed random variables have the common continuous distribution function F(x), specified in advance. In principle such tests will give confidence regions for the unknown distribution function, for if we have a test (based on the n observations) for every F(x) the confidence region will consist of those F(x) for which the corresponding hypotheses are not rejected. (Author)
AN INVENTORY PRICING PROBLEM(
Book
)
1 edition published in 1962 in English and held by 1 WorldCat member library worldwide
The optimum behavior of a perso who is forced to make a decision, or a se of ci io b for p cifi deadline is analyzed. The problem considered is one of a merchant elling goods to the public walking past his store. (Author)
1 edition published in 1962 in English and held by 1 WorldCat member library worldwide
The optimum behavior of a perso who is forced to make a decision, or a se of ci io b for p cifi deadline is analyzed. The problem considered is one of a merchant elling goods to the public walking past his store. (Author)
Reports issued by D.A. Darling on the progress and accomplishments of the statistical project by
D. A Darling(
Book
)
1 edition published in 1943 in English and held by 1 WorldCat member library worldwide
1 edition published in 1943 in English and held by 1 WorldCat member library worldwide
Continuous stochastic processes by
D. A Darling(
Book
)
1 edition published in 1947 in English and held by 1 WorldCat member library worldwide
1 edition published in 1947 in English and held by 1 WorldCat member library worldwide
Some relations between potential theory and the wave equation by
D. A Darling(
Book
)
2 editions published in 1960 in English and held by 1 WorldCat member library worldwide
Solutions to the Dirichlet and Neumann problems for the region exterior to the intersection of two regions whose individual electrostatic Green's functions are known are developed. The method is applied specifically to obtain solutions for the exterior of a solid finite circular cone with a spherical cap. The solutions to the vector and scalar wave equations for long wavelengths can be expressed in terms of these Dirichlet and Neumann solutions
2 editions published in 1960 in English and held by 1 WorldCat member library worldwide
Solutions to the Dirichlet and Neumann problems for the region exterior to the intersection of two regions whose individual electrostatic Green's functions are known are developed. The method is applied specifically to obtain solutions for the exterior of a solid finite circular cone with a spherical cap. The solutions to the vector and scalar wave equations for long wavelengths can be expressed in terms of these Dirichlet and Neumann solutions
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Darling, D. A. 1915
Darling, Donald 1915
Darling, Donald A.
Darling, Donald Allen 1915
Donald A. Darling statistico statunitense
Donald Allan Darling Amerikaans statisticus (19152014)
Donald Allan Darling USamerikanischer Statistiker
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