摘要:

SummaryThis note describes a numerical investigation of the normal and χ2‐approximations to the hypergeometric distribution, which leads to a surprisingly simple foot rule. If n and r are the two smaller marginal totals, then for the tails of the distribution up to about a probability of 0.07, the normal approximation will in nearly all cases be better than the χ2ifn+r1/2N(whereNis the grand marginal total) and worse otherwise. Although the two approximations are nearly equivalent, thisfootrule is so simple that it seems worth publish

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00560.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

摘要:

SummaryThe well‐known relation between random division of an interval and the Poisson process is interpreted as a Laplace transformation. With the use of this interpretation a number of (in part known) results is derived very easil

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00561.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

摘要:

Summary.This paper generalizes an interrupted Poisson process first studied by ZAAT [8] and later by RUNNENBURG and VERVAAT [7]. The process is obtained by combining two independent stochastic processes on the non‐negative real axis. The first of these processes is a stationary Poisson process with intensity Λ and the second an alternating renewal process [1] dividing the axis in a‐ and b‐intervals alternatively. By omitting those points of the stationary Poisson process that fall in b‐intervals we create a new point process that we prefer to call a “thinned Poisson process”. The alternating renewal process is determined by the distribution functions A and B of the lengths of the a‐ and b‐intervals which are not the first interval to the right ofO and by an “initial distribution” (p, A0, B0), where p is the probability of starting with an a‐interval in 0, A0the distribution function of the length of the first a‐interval provided that we begin with an a‐interval in 0, and B0the distribution function of the first b‐interval provided that we begin with a b‐interval in 0.It is here shown that there always exist initial distributions for which the distribution function of the length of an interval between two successive points in the thinned Poisson process is the same for all intervals, and the class of initial distributions with this property is obtained. The common distribution function G of these lenghts has Laplace‐Stieltjes transform G as given in (3.15); it turns out that G depends on A, B and Λ only.For any initial distribution the distribution function of the distance between the nth and the (n + l)st point to the right ofO in the thinned Poisson process tends to the distribution function G as n tends to infinity. Finally the covariance of two successive distances between three successive points in the thinned Poisson process is studied. Some examples are given in which both positiv

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00562.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

摘要:

SummaryThe paper contains an elementary introduction, using no measure theory, to the theory of conditional expectations and martingales.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00563.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00564.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00565.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY

摘要:

Book reviewed in this article:“Netwerkplanning volgens PERT”, Oorspronkelijke uitgave Federal Electric Corporation. Voor Nederland bewerkt door H. POOLMAN Jr en TH. M. FEMER.Group representations and applied probability, E. J. HANNANWahrscheinlichkeit und Information, A. M. YAGLOM und J. M. YAGLOMLinear programming and the theory of the Arm, K. E. BOULDING en W. A. SPIVEYEinftihring in die matbematische Statistik, L. SCHMETTERERRecent results in information theory, S. KOTZFormeln und Tabellen der mathematischen Statistik, U. GRAF, H. J. HENNINO en K. STANGEThe elements of probability theory and some of its applications, H. CRAMERQuality control and industrial statistics, ACHESON J. DUNCANMéthodes Statistiques de ľéonometrie, E. MALINVAUDWahrscheinlichkeitstheorie, H. RICHTERLinear statistical inference and its applications, C. R. RAO, WileyGebouw en getal ‐ capita aselecta uit het bouwen en de statistiek, aangeboden aan JAN VAN ETTINGERThe Mathematical Approach to Biology and Medicine, NORMAN T. J. BAILEYZum Problem der Produktionsplanung in Ein‐ und Mehrproduktunternehmen, W. DINKEL‐BACH[1] Die grundlagen der Theorie der Markoffschen Prozesse, E. B. DYNKYN[1a] Theory of Markov processes, E. B. DYNKYN[1b] Markov Processes, 2 delen, E. B. DYNKYN[2] Probability and related topics in physical sciences, M. KAC, Interscience publ., London, 1959.[3] Markov chains with stationary transition probabilities, K. L. CHUNG[4] Probabilités et potentiel, P. A. MEYER[4a] Probability and potentials, P. A. MEYER[4b] Processus de Markov, P. A. MEYER[5] Intégration, N. BOURBAKI[6] Principles of random walk, F. SPITZER[7] An introduction to probability theory and its applications, second edi

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1967.tb00566.x

出版商:Blackwell Publishing Ltd    

年代:1967

数据来源: WILEY