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1.
S. Subba Rao 《Metrika》1969,14(1):101-116
Summary This paper considers the effect of postponable interruptions on aM/G/1 queueing process where customers balk with probabilityn/N (n=0, 1, 2, …,N) and renege after having waited for a random length of time. The busy period process in which transitions from any state
(m, n) to any other state are permitted without an intermediate passage to the empty state, is investigated employing the
supplementary variable method and discrete transforms. Later, the general process in which busy periods alternate with idle
periods has been discussed in terms of the busy period process and renewal distributions and finally the ergodic properties
of the general process studied by appealing to some results of renewal theory. 相似文献
2.
Dr. P. N. Rathie 《Metrika》1972,18(1):216-219
Equivalence of the generalized entropyH
β (P, Φ
t
) defined in this paper andKapur’s entropy of orderα and typeβ, ie.H
α
β
(P), is established. The results given recently byCampbell follow as special cases.
International Conference on System Sciences, Honolulu, January 1968. 相似文献
3.
R. Natarajan 《Metrika》1968,13(1):104-122
Summary This paper gives an analysis of a system withN
1 components of one type andN
2 components of another type in parallel with uninterrupted running times of each component following exponential distribution
and the repair time following arbitrary distribution. The head of the line and preemptive resume priority disciplines have
been imposed on the repair of the components. The busy period process is investigated first using the supplementary variable
method. Then the general time dependent process in which busy periods alternate with idle periods has been studied in terms
of the busy period probabilities and probability of finding the repair facility idle at timet. Finally, the long-run availability of the system in terms of the steady state probabilities for the two cases of priority
disciplines has been obtained. 相似文献
4.
5.
Prof. Dr. A. Irle 《Metrika》1987,34(1):107-115
Summary LetX
1,X
2, ... form a sequence of martingale differences and denote byZ(a, α) = sup n (S
n
−an
α)+ the largest excess forS
n
=X
1 + ... +X
n
crossing the boundaryan
α. We give a sufficient condition for the finiteness ofEZ(a, α)β which is formulated in terms of bounds forE(X
i
+
p
andE(|X
i
|γ|X
1, ...,X
i-1), whereα, β, γ, p are suitably related. This general result is then applied to the case of independent random variables. 相似文献
6.
B. M. Bennett 《Metrika》1970,15(1):6-8
Summary LetN=[n
ij
] (i=1, …,r;j=1, …,c) be the matrix of observed frequencies in anr×c contingency table fromr possibly different multinomial populations with respective probabilitiesp
i
=(p
i1, …,p
ic
).Freeman andHalton have proposed an exact conditional test for the hypothesisH
0 :p
i
=(p
1, …p
c
) of the exact test is derived. Numerical values forβ(p) were previously computed for the special case:r=3,c=2 [Bennett andNakamura, 1964]. 相似文献
7.
C. Di Guilmi F. Clementi T. Di Matteo M. Gallegati 《Journal of Economic Interaction and Coordination》2008,3(1):43-57
This paper uses firm-level data recorded in the Amadeus database to investigate the distribution of labour productivity in different European countries. We find that the upper tail
of the empirical productivity distributions follows a decaying power-law, whose exponent α is obtained by a semi-parametric estimation technique recently developed by Clementi et al. [Physica A 370(1):49–53, 2006].
The emergence of “fat tails” in productivity distribution has already been detected in Di Matteo et al. [Eur Phys J B 47(3):459–466,
2005] and explained by means of a model of social network. Here we show that this model is tested on a broader sample of countries
having different patterns of social network structure. These different social attitudes, measured using a social capital indicator,
reflect in the power-law exponent estimates, verifying in this way the existence of linkages among firms’ productivity performance
and social network. 相似文献
8.
Bernhard F. Arnold 《Metrika》1996,44(1):119-126
In this paper an approach is presented how to test fuzzily formulated hypotheses with crisp data. The quantitiesα andβ, the probabilities of the errors of type I and of type II, are suitably generalized and the concept of a best test is introduced.
Within the framework of a one-parameter exponential distribution family the search for a best test is considerably reduced.
Furthermore, it is shown under very weak conditions thatα andβ can simultaneously be diminished by increasing the sample size even in the case of testingH
0 against the omnibus alternativeH
1: notH
0, a result completely different from the case of crisp setsH
0 andH
1: notH
0. 相似文献
9.
D. G. Kabe 《Metrika》1970,15(1):15-18
Summary
Likes obtains the distributions ofDixon’s statistics for an exponential population and tabulates upper 100α% points (α=0.1, 0.05, 0.01) of some of these distributions.
The distribution of these statistics can be expressed in terms of finite series of beta functions and hence the probabilities
of the rejection of suspected observed outliers may be easily calculated on a desk calculator. Thus we may avoid the difficult
task of tabulating 100α% values of these statistics. 相似文献
10.
Minimax estimators andΓ-minimax estimators for a bounded normal mean under the lossl
p (θ, d)=|θ-d|p
Summary Let the random variableX be normal distributed with known varianceσ
2>0. It is supposed that the unknown meanθ is an element of a bounded intervalΘ. The problem of estimatingθ under the loss functionl
p
(θ, d)=|θ-d|
p
p≥2 is considered. In case the length of the intervalθ is sufficiently small the minimax estimator and theΓ(β, τ)-minimax estimator, whereΓ(β, τ) represents special vague prior information, are given. 相似文献
11.
Summary We consider in this paper the transient behaviour of the queuing system in which (i) the input, following a Poisson distribution,
is in batches of variable numbers; (ii) queue discipline is ‘first come first served’, it being assumed that the batches are
pre-ordered for service purposes; and (iii) service time distribution is hyper-exponential withn branches. The Laplace transform of the system size distribution is determined by applying the method of generating functions,
introduced in queuing theory byBailey [1]. However, assuming steady state conditions to obtain, the problem is completely solved and it is shown that by suitably
defining the traffic intensity factor,ϱ, the value,p
0, of the probability of no delay, remains the same in this case of batch arrivals also as in the case of single arrivals.
The Laplace transform of the waiting time distribution is also calculated in steady state case from which the mean waiting
time may be calculated. Some of the known results are derived as particular cases. 相似文献
12.
Dr. Gustav Feichtinger 《Metrika》1972,18(1):35-55
Zusammenfassung In diesem Beitrag zur statistischen Lerntheorie (Stimulus Sampling Theorie) wird einN-elementiges „Pattern“-Modell mitr verfügbaren Antworten und nichtkontingenter Verst?rkungsvorschrift diskutiert. Um von der lerntheoretischen Literatur nicht
zu sehr abh?ngig zu sein, wird zun?chst ein kanpper überblick über die Grundbegriffe der Stimulus Sampling Theorie gegeben.
Der Vorgang des „Wahrscheinlichkeitslernens“ wird mittels des Reiz-Antwort-Schemas der statistischen Lerntheorie erkl?rt.
Durch die Einführung der sogenannten bedingenden Zust?nde gelangt die Theorie derMarkovketten zur Anwendung. Schlie?lich wird das Problem der übereinstimmung von empirischen Daten aus Lernexperimenten mit den
aus der Theorie abgeleiteten anhand von Sequentialstatistiken studiert.
Summary In this contribution to the statistical learning theory (stimulus sampling theory) aN-element pattern model withr availables responses and noncontingent reinforcement schedule is discussed. First a short survey of the principles of the stimulus sampling theory is given. The process of „probability learning“ is explained by the stimulus-response model of the statistical theory of learning. By the introduction of the so-called conditioning states the theory ofMarkov chains may be applicated. Finaly, the goodness-of-fit between empirical data of learning experiments and predicted statistics is studied on the basis of sequential predictions.相似文献
13.
P. Fischer 《Metrika》1972,18(1):199-208
Summary We shall deal with the inequality (2) and we prove among others the following results. Every solution of the inequality (2)
is monotone increasing. Every solution of the inequality (2) is differentiable ifn≥3. A functionf satisfies the inequality (3) if and only if its saltus part and absolutely continuous part satisfy also the inequality (3).
We give the general solution of (3) in the field of saltus function. Finally by the help of [Muszély] we give the general solution of (3). This results are generalisations of one ofJ. Aczél andJ. Pfanzagl.
Zusammenfassung Wir betrachten die Ungleichung (2) und beweisen die folgenden Ergebnisse. Die allgemeine L?sung der Ungleichung (2) ist monoton wachsend. Die allgemeine L?sung der Ungleichung (2) ist differenzierbar im Falle wennn≥3 ist. Wir geben also die allgemeine L?sung der Ungleichung (3) mit Hilfe von [Muszély]. Diese Ergebnisse sind Verallgemeinerungen des Resultats vonJ. Aczél undJ. Pfanzagl.相似文献
14.
In literature, Williams Square change-over designs balanced for first residual effects of treatments have been proved to
be universally optimal. Here, an attempt has been made to show that these designs are robust against missing of last α [≤v−1; v being the number of periods in the design for v treatments] observations from an experimental unit.
Received May 2000 相似文献
15.
Arturo J. Fernández 《Metrika》2000,50(3):211-220
In this paper, the maximum likelihood predictor (MLP) of the kth ordered observation, t
k, in a sample of size n from a two-parameter exponential distribution as well as the predictive maximum likelihood estimators (PMLE's) of the location and scale parameters, θ and β, based on the observed values t
r, …, t
s (1≤r≤s<k≤n), are obtained in closed forms, contrary to the belief they cannot be so expressed. When θ is known, however, the PMLE of β and MLP of t
k do not admit explicit expressions. It is shown here that they exist and are unique; sharp lower and upper bounds are also
provided. The derived predictors and estimators are reasonable and also have good asymptotic properties. As applications,
the total duration time in a life test and the failure time of a k-out-of-n system may be predicted. Finally, an illustrative example is included.
Received: August 1999 相似文献
16.
Pranab Kumar Sen 《Metrika》1972,18(1):234-237
Summary For independently distributed error components, the asymptotic relative efficiency (A.R.E.) ofFriedman’sx
r
2
-tests with respect to the classical analysis of variance test has been studied byElteren andNoether andSen [1967]. The present note extends these results to the case of correlated errors arising in some random-effects or mixed-effects
models.
Work supported by the U.S. Army Research Office, Durham, Grant DA-ARO-D-31-124-G 746. 相似文献
17.
Summary Dynamic exponential family regression provides a framework for nonlinear regression analysis with time dependent parametersβ
0,β
1, …,β
t, …, dimβ
t=p. In addition to the familiar conditionally Gaussian model, it covers e.g. models for categorical or counted responses. Parameters
can be estimated by extended Kalman filtering and smoothing. In this paper, further algorithms are presented. They are derived
from posterior mode estimation of the whole parameter vector (β′0, …,β′t) by Gauss-Newton resp. Fisher scoring iterations. Factorizing the information matrix into block-bidiagonal matrices, algorithms
can be given in a forward-backward recursive form where only inverses of “small”p×p-matrices occur. Approximate error covariance matrices are obtained by an inversion formula for the information matrix, which
is explicit up top×p-matrices.
Heinz Leo Kaufmann, my friend and coauthor for many years, died in a tragical rock climbing accident in August 1989. This
paper is dedicated to his memory. 相似文献
18.
Let (W
n
,n ≥ 0) denote the sequence of weak records from a distribution with support S = { α0,α1,...,α
N
}. In this paper, we consider regression functions of the form ψ
n
(x) = E(h(W
n
) |W
n+1 = x), where h(·) is some strictly increasing function. We show that a single function ψ
n
(·) determines F uniquely up to F(α0). Then we derive an inversion formula which enables us to obtain F from knowledge of ψ
n
(·), ψ
n-1(·), h(·) and F(α0). 相似文献
19.
Prof. Dr. J. Pfanzagl 《Metrika》1970,15(1):30-39
Summary
Lehmann [p. 83] has shown that some families of probability measures with monotone likelihood ratios (m.l.r.) admit median unbiased
estimates which are optimum in the sense that among all median unbiased estimates they minimize the expected loss for any
loss function which assumes its minimal value zero for the “true” parameter value and is nondecreasing as the parameter moves
away from the true value in either direction. This very strong optimum property was proved under the assumption that all probability
measures of the m.l.r.-family have continuous distribution functions, that they are mutually absolutely continuous and that
each element of the support is the median of somep-measure of the family. This result does therefore not cover important cases such as the binomial families or thePoisson family.
The purpose of the present paper is to show the existence ofrandomized median unbiased estimates with the same optimum property for m.l.r.-families which are closed and connected with respect
to the strong topology. Such families are always dominated. We do, however, neither assume that thep-measures are mutually absolutely continuous nor that the distribution functions are continuous. We remark that the use of
randomized estimates is indispensable here because nonrandomized median unbiased estimates do not always exist in the general
case. 相似文献
20.
Prof. Dr. A. Adam 《Metrika》1965,9(1):163-194
Zusammenfassung Die Statistik wird als ein formalisiertes Sprachsystem gedeutet und verschiedene Statistikalgorithmen werden über einenBooleschen Verband gebildet. Es werden nur nichtstochastische Probleme behandelt.
Der erste Teil dieser Abhandlung über eine attributive Statistik alsBoolescher Verband wurde im Heft Nr. 2 (1964) der Metrika als Festbeitrag zum 80. Geburtstag des Jubilars Hofrat Prof. Dr. Dr. h. c.Wilhelm Winkler ver?ffentlicht. Statistische Ma?verb?nde erscheinen über eine quasiadditive Bewertung eingeführt. Im vorliegenden zweiten Teil der Arbeit werden die Beziehungen der Statistik zurβ-Informationstheorie und einer speziellen Semiotik kurz er?rtert und die Algebraisierungs-beziehungsweise Geometrisierungsversuche betreffend die statistischen Forschungsmethoden weitergeführt. 相似文献
Summary Statistic is considered a formalized language system. Some statistical algorithms are interpreted in aBoolean lattice. Only nonstochastical problems are considered.
Der erste Teil dieser Abhandlung über eine attributive Statistik alsBoolescher Verband wurde im Heft Nr. 2 (1964) der Metrika als Festbeitrag zum 80. Geburtstag des Jubilars Hofrat Prof. Dr. Dr. h. c.Wilhelm Winkler ver?ffentlicht. Statistische Ma?verb?nde erscheinen über eine quasiadditive Bewertung eingeführt. Im vorliegenden zweiten Teil der Arbeit werden die Beziehungen der Statistik zurβ-Informationstheorie und einer speziellen Semiotik kurz er?rtert und die Algebraisierungs-beziehungsweise Geometrisierungsversuche betreffend die statistischen Forschungsmethoden weitergeführt. 相似文献