共查询到20条相似文献,搜索用时 46 毫秒
1.
W. H. Somermeiier 《Statistica Neerlandica》1957,11(3):153-160
The recently repeated assertion that in correlation analysis it makes little difference whether one variable (x2 ) is used instead of another one (x3 ), provided the coefficient of correlation (r23 ) between x2 and x3 is high, is scrutinized.
To that purpose the ranges of coefficients of correlation with respect to the substitute variable are expressed in formula 3. Moreover, by way of example, extreme values of coefficients of simple correlation (r13 and r34 ), of multiple correlation (R1.34 and R3.14 ) and of regression (α13 and α14 , α31 and α34 ) relating to the substitute variable, are calculated on the basis of empirical values of coefficients of simple correlation relating to the substituted and the remaining variables.
The outcome of those calculations are summarized in the tables 1 and 3, and in the graph.
Table 1 presents ranges of r13 for given values of r12 and r23 , table 3 shows extreme values of coefficients of single and multiple correlation and regression in case an additional variable x4 is introduced and r12 , r14 , r24 and r23 are given. The graph shows an ellipse as the boundary of the inner closed domain of compatible values of r13 and r34 .
Those results clearly indicate the need for caution in substituting one variable by another. 相似文献
To that purpose the ranges of coefficients of correlation with respect to the substitute variable are expressed in formula 3. Moreover, by way of example, extreme values of coefficients of simple correlation (r
The outcome of those calculations are summarized in the tables 1 and 3, and in the graph.
Table 1 presents ranges of r
Those results clearly indicate the need for caution in substituting one variable by another. 相似文献
2.
Maximum entropy or minumum information distributions have their flexibilities severely curtailed if R or R+ is the domain and α is imposed as a Lebesgue measure. Tremendous flexibility is gained by removing these restrictions. 相似文献
3.
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 hn 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 hn . In section 2 it is shown that hn is asymptotically normal.
In the sequel we suppose μ= 0 and = 1, i.e. we consider only the "central" distribution. Note that hn can be used as a test statistic replacing Student's t. In that case the central hn is all that is needed. 相似文献
The random variable
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
In the sequel we suppose μ= 0 and = 1, i.e. we consider only the "central" distribution. Note that h
4.
《Statistica Neerlandica》1960,22(3):151-157
Summary "Stratificationprocedures for a typical auditing problem".
During the past ten years, much experience was gained in The Netherlands in using random sampling methods for typical auditing problems. Especially, a method suggested by VAN. HEERDEN [2] turned out to be very fruitful. In this method a register of entries is considered to be a population of T guilders, if all entries total up to T guilders. The sample size n0 is determined in such a way that the probability β not to find any mistake in the sample, if a fraction p 0 or more of T is incorrect, is smaller than a preassigned value β0 . So n 0 should satisfy (l- p )n0 ≤β0 for p ≥ p 0 . A complication arises if it is not possible to postpone sampling until the whole population T is available. One then wants to take samples from a population which is growing up to T . Suppose one is going to take samples n i from e.g. r subpopulations
Using the minimax procedure, it is shown, that in this case one should choose the sizes ni equal to ( T i / T ) n 0 . The minimax-value of the probability not to find any incorrect guilder in the r samples, taken together is equal to β0 . 相似文献
During the past ten years, much experience was gained in The Netherlands in using random sampling methods for typical auditing problems. Especially, a method suggested by VAN. HEERDEN [2] turned out to be very fruitful. In this method a register of entries is considered to be a population of T guilders, if all entries total up to T guilders. The sample size n
Using the minimax procedure, it is shown, that in this case one should choose the sizes n
5.
In this paper, we use the Bayesian approach to study the problem of selecting the best population among k different populations π1 , ..., πk (k≥2) relative to some standard (or control) population π0 . Here, π0 is considered to be the population with the desired characteristics. The best population is defined to be the one which is closest to the ideal population π0 . The procedure uses the idea of minimizing the posterior expected value of the Kullback–Leibler (KL) divergence measure of π i from π0 . The populations under consideration are assumed to be multivariate normal. An application to regression problems is also presented. Finally, a numerical example using real data set is provided to illustrate the implementation of the selection procedure. 相似文献
6.
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 … x jk in the systems j,… j k respectively. 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 … jk }. The latter performance is maximized in order to determine { j 1 *.,., jk * }. 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. 相似文献
7.
A. J. J. Talman 《Statistica Neerlandica》1979,33(3):143-150
Abstract An M/G/l queueing system with removable server is considered. The following costs are incurred: a holding cost of h per unit time per customer in the system, a cost of rl (r2 ) per unit time when the service mechanism is on (off) and a fixed cost of K1 ,(K2 ,) for turning it on (off).
In this paper we shall give a very simple proof for the well known and intuitively obvious fact that the best N-policy is optimal for the average cost criterion among the class of all policies by first proving that the average cost formula of that policy and its relative cost function satisfy the optimality equation for the average cost criterion. The optimality of the best N-policy is then an immediate consequence. 相似文献
In this paper we shall give a very simple proof for the well known and intuitively obvious fact that the best N-policy is optimal for the average cost criterion among the class of all policies by first proving that the average cost formula of that policy and its relative cost function satisfy the optimality equation for the average cost criterion. The optimality of the best N-policy is then an immediate consequence. 相似文献
8.
Arnoud van Rooij 《Statistica Neerlandica》2002,56(2):206-213
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 fM (M>0) derived from F f by the formula fM (x) =( F( εM · F f ))(− x );, where the εM 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 (fM , 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. 相似文献
9.
《Statistica Neerlandica》1958,12(2):63-73
Laten T1 en T2 twee toetsen zijn voor dezelfde hypothese θ=θ0 betreffende de waarde van een parameter θ, Zij verder de onbetrouwbaarheidsdrempel van beide toetsen gelijk aan α en het onderscheidingsvermogen tegen de alternatieve hypothese θ=θ1 geliik aan 1-β. Indien toets T1 nu n1 waarnemingen vergt en toets T2 n2 waarnemingen, dan wordt de relatieve doeltreffendheid (Eng.: efficiency) van toets T1 ten opzichte van toets T2 (als toetsen voor θ=θ0 tegen θ=θ1 gegeven door: e = n2 /n1 . Indien men de waarde van θ1 op een bepaalde wijze naar θ0 laat convergeren bij toenemende n1 , is het in vele gevallen, door gebruik te maken van een stelling van α en β Deze limiet-waarde wordt de asymptotische relatieve doeltreffendheid (volgens Pitman) genoemd. In dit artikel wordt een overzicht gegeven van hetgeen bekend is over de asymptotische relatieve doeltreffendheid van een aantal verdelingsvrije toetsen ten opzichte van de corresponderende standaardtoetsen.
De conclusie van de schrijver is, dat men bij het gebruik van verdelingsvrije methoden met een hoge doeltreffendheid (bijv. de symmetrietoets en de twee-steek-proeven-toets van Wilcoxon, de toets van Kruskal voor k steekproeven en de methode van m rangschikkingen) slechts zeer weinig informatie kan verliezen en dat zelfs het gebruik van minder doeltreffende verdelingsvrije methoden gerechtvaardigd kan zijn. 相似文献
De conclusie van de schrijver is, dat men bij het gebruik van verdelingsvrije methoden met een hoge doeltreffendheid (bijv. de symmetrietoets en de twee-steek-proeven-toets van Wilcoxon, de toets van Kruskal voor k steekproeven en de methode van m rangschikkingen) slechts zeer weinig informatie kan verliezen en dat zelfs het gebruik van minder doeltreffende verdelingsvrije methoden gerechtvaardigd kan zijn. 相似文献
10.
We investigate the validity of the bootstrap method for the elementary symmetric polynomials S ( k ) n =( n k )−1 Σ1≤ i 1 < ... < i k ≤ n X i 1 ... X i k of i.i.d. random variables X 1 , ..., X n . For both fixed and increasing order k , as n→∞ the cases where μ=E X 1 [moe2]0, the nondegenerate case, and where μ=E X 1 =0, the degenerate case, are considered. 相似文献
11.
Consider a sequence of random points placed on the nonnegative integers with i.i.d. geometric (1/2) interpoint spacings y i . Let x i denote the numbers of points placed at integer i . We prove a central limit theorem for the partial sums of the sequence x 0 y 0 , x 1 y 1 , . . . The problem is connected with a question concerning different bootstrap procedures. 相似文献
12.
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 {Xn } generated according to the scheme Xn =α° X n -i +en , where α° X n-1 denotes a sum of Xn - 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. 相似文献
13.
Assume k ( k ≥ 2) independent populations π1 , π2 μk are given. The associated independent random variables Xi ,( i = 1,2,… k ) are Logistically distributed with unknown means μ1 , μ2 , μk 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. 相似文献
14.
J. A. Wellner 《Statistica Neerlandica》1994,48(3):201-207
Prenctice and Cai recently introduced and studied the function C defined as the covariance function of the two marginal counting process martingales of a pair of dependent survival times (T1 , T2 ). They show that the function C together with the marginal distributions determines the joint survival function F of (T1 , T2 ). In this note we show how the key characterizing equation of Prentice and Cai yields a formula for the covariance of T1 and T2 in termsof the marginal mean residual life functions and C. The resulting formula generalizes a formula for the variance of a one-dimensional random variable Tdueto Pyke (1965). We also explore several generalizations of the covariance formula, and obtain a valid k-dimensional version of the Prentice and Cai formula. 相似文献
15.
We generalize the extreme value analysis for Archimedean copulas (see Alink , Löwe and Wüthrich , 2003) to the non-Archimedean case: Assume we have d ≥2 exchangeable and continuously distributed risks X 1 ,…, X d . Under appropriate assumptions there is a constant q d such that, for all large u , we have . The constant q d describes the asymptotic dependence structure. Typically, q d will depend on more aspects of this dependence structure than the well-known tail dependence coefficient. 相似文献
16.
M. Ahsanullah 《Statistica Neerlandica》1988,42(3):193-198
Suppose X1 , X2 , Xm is a random sample of size m from a population with probability density function f (x), x > 0), and let X1, m < × 2, m <… < Xm, m be the corresponding order statistics.
We assume m is an integer-valued random variable with P( m = k ) = p (1- p )k-1 , k = 1,2,… and 0 < p < 1. Two characterizations of the exponential distribution are given based on the distributional properties of Xl, m . 相似文献
We assume m is an integer-valued random variable with P( m = k ) = p (1- p )
17.
A. J. Stam 《Statistica Neerlandica》1978,32(2):81-91
Summary Two random samples of size n are taken from a set containing N objects of H types, first with and then without replacement. Let d be the absolute (L1 -)distance and I the K ullback -L eibler information distance between the distributions of the sample compositions without and with replacement. Sample composition is meant with respect to types; it does not matter whether order of sampling is included or not. A bound on I and d is derived, that depends only on n, N, H. The bound on I is not higher than 2 I. For fixed H we have d 0, I 0 as N if and only if n/N 0. Let W r be the epoch at which for the r-th time an object of type I appears. Bounds on the distances between the joint distributions of W 1 ., W r without and with replacement are given. 相似文献
18.
Abstract If X 1 , X 2 ,… are exponentially distributed random variables thenσ∞ k= 1 Xk =∞ with probability 1 iff σ∞ k= 1 EXk =∞. This result, which is basic for a criterion in the theory of Markov jump processes for ruling out explosions (infinitely many transitions within a finite time) is usually proved under the assumption of independence (see FREEDMAN (1971), p. 153–154 or BREI-MAN (1968), p. 337–338), but is shown in this note to hold without any assumption on the joint distribution. More generally, it is investigated when sums of nonnegative random variables with given marginal distributions converge or diverge whatever are their joint distributions. 相似文献
19.
《Statistica Neerlandica》1960,22(2):103-118
Summary A branch and bound algorithm is given to solve the following problem: To each pair of elements (i,j) from a set X ={l,…, n } a number r ij with r ij ≥ 0, r ij = r ij and r ij = 0 has been assigned. Find a prescribed number of disjoint subsets P 1 …, P m from X , such that
Experiments indicate that an optimal solution is usually found in a small number of iterations, but the verification may be rather time consuming.
The algorithm may be used to find the minimum value of m for which a partitioning of X with z = 0 exists. The algorithm appears to be efficient for finding this 'chromatic number of a graph'. 相似文献
Experiments indicate that an optimal solution is usually found in a small number of iterations, but the verification may be rather time consuming.
The algorithm may be used to find the minimum value of m for which a partitioning of X with z = 0 exists. The algorithm appears to be efficient for finding this 'chromatic number of a graph'. 相似文献
20.
H. J. H. Tuenter 《Statistica Neerlandica》2000,54(3):374-376
We use Euler's difference lemma to prove that, for θ > 0 and 0 ≤λ < 1, the function P n defined on the non-negative integers by
P n (θ, λ) = [θ(θ + n λ) n −1 / n !]e− n λ−θ
defines a probability distribution, known as the Generalized Poisson Distribution. 相似文献
P
defines a probability distribution, known as the Generalized Poisson Distribution. 相似文献