Renewal Point Research Articles

La productivité agricole dans le monde depuis la révolution néolithique : ruptures et stagnations

If 1948 is the birth date of the SFER, and the starting point of a significant renewal in the french though as applied to agricultural economics, it is also the beginning of a fascinating period of technical progress in western countries agricultures, especially the French one. No similar situation never occured in human history. The coïncidence is not fortuitous, for, obviously, the second of these two events impiged upon the first. This is why a few facts are to be recoiled before tackling the evolution of ideas. The most spectacular of them is the increase in the productivity of labour. Between 1950 and 1990, it grew more than between the neolthic revolution and 1950. This growth is more important in western than in thirld world countries, and in agriculture than in industry.

An Infinite Dam with a Time-Dependent Release Rule

An infinite dam with discrete inputs arriving at times 0 = T0 < T1 <…< Tn <… is considered, where {Tn;n = 0,1,2,…} forms a renewal process. There is a random release from the dam during the interrenewal times which depends on the content as well as on the length of the time after the last input. A relation is derived that connects the content distribution at any time t to that when t is a renewal point. This relation is used to obtain the content distribution in the limiting case and in the transient case. The probability of emptiness is obtained and an integral equation is derived for the probability of first emptiness in a special case.

Random sampling of continuous-parameter stationary processes: Statistical properties of joint density estimators

Let { X( t), −∞ < t < ∞} be a real-valued stationary process with a bivariate probability density function f( x 1, x 2; t), t > 0, and let { t j } be a renewal point processes on [0, ∞). Estimates f ̂ n(x 1, x 2; t) of f( x 1, x 2; t), based on the discretetime observations { X( t j ), t j } j = 1 n , are considered and their statistical properties are investigated. The quadratic-mean consistency of f ̂ n(x 1, x 2; t) and central limit theorems for f ̂ n(x 1, x 2; t) are established for mixing processes { X( t), −∞ < t < ∞}. Similar results are obtained for estimators of multivariate densities of the process { X( t), −∞ < t < ∞}.

Role of primary excitation statistics in the generation of antibunched and sub-Poisson light

We examine the coherence properties of stationary light obtained by the superposition of nonstationary independent emissions occurring at random space–time points. The positions of the points are independent and uniformly distributed over the volume of the source. The emission times fluctuate in accordance with a stationary renewal point process. This process admits of super-Poisson, sub-Poisson, or Poisson behavior. The individual emissions are assumed to be in a coherent, chaotic, or n state. The statistical nature of the random-emission space–time points plays an important role in determining the coherence properties and photon statistics of the total field. This is manifested in the normalized second-order correlation function, which turns out to have the usual form for chaotic light with two additional terms. The first of these is determined by the statistical nature of the individual emissions (it is positive for coherent or chaotic, but zero for single-photon, emissions). The second term is governed by the statistics of the primary excitations (it is positive for super-Poisson, zero for Poisson, and negative for sub-Poisson excitations). Both additional terms become small for light with a high degeneracy parameter (many total photons per emission lifetime). The behavior of the light is then asymptotically chaotic. In the opposite limit, when the degeneracy parameter is small (or the emissions are instantaneous), the correlation properties of the primary excitations are directly transferred to the correlation properties of the photons. The first-order spatial-coherence properties of the field turn out to be identical with those of chaotic light (i.e., the van Cittert–Zernike theorem is obeyed), although the second-order properties differ. The photon-counting distribution reflects the character of the correlation function. Thus sub-Poisson primary excitations, together with n-state emissions, can lead to sub-Poisson photon counts under certain conditions. Such nonclassical light may be made arbitrarily intense if interference effects are eliminated by detecting many spatial modes. As an example of our theory, we cite a Franck–Hertz experiment excited by a space-charge-limited electron beam. If the electron excitations are represented as a sub-Poisson renewal point process, and the photon emissions as one-photon states, the light generated should be antibunched and sub-Poisson.

Analysis of a Cyclic Placement Scheme

This paper considers a simple scheme for dynamic storage allocation and shows that an analysis is possible through use of probability theory and the theory of renewal point processes. A placement scheme is considered which attempts to keep storage highly compact and obviates the need for time consuming scanning of free storage lists. An analysis of the storage loss due to fragmentation is presented together with the results of simulation experiments. The study indicates that, although the chosen scheme is amenable to theoretical analysis, it is inferior in performance to other well known schemes for dynamic storage allocation. A modification to the scheme is presented which gives utilization comparable with first fit but has lower free list searching overheads.

Regenerative multivariate point processes

A class of stationary multivariate point processes is considered in which the events of one of the point processes act as regeneration points for the entire multivariate process. Some important properties of such processes are derived including the joint probability generating function for numbers of events in an interval of fixed length and the asymptotic behaviour of such processes. The general theory is then applied in three bivariate examples. Finally, some simple monotonicity results for stationary and renewal point processes (which are used in the second example) are proved in two appendices.

Regenerative multivariate point processes

A class of stationary multivariate point processes is considered in which the events of one of the point processes act as regeneration points for the entire multivariate process. Some important properties of such processes are derived including the joint probability generating function for numbers of events in an interval of fixed length and the asymptotic behaviour of such processes. The general theory is then applied in three bivariate examples. Finally, some simple monotonicity results for stationary and renewal point processes (which are used in the second example) are proved in two appendices.

Stochastic processes with imbedded marked point processes (pmp) and thcir application in queneing

In generalization of special cases of the literature a class of stochastic processes (PMP) is defined with an imbedded stochastic marked point process of “basic points” which must not be renewal points. A theorem (“intensity conservation principle”) has been proved concerning a relation between stationary distribution of PMP at arbitrary points in time and distributions and intensities connected with the basic points. This relationship simultaneously yields a general method for determination of stationary quantities at arbitrary points in time by means of the corresponding “imbedded” quantities. Some applications to concrete queueing systems have been demonstrated, where arrival or departure epochs of customers are used as basic points. Under weaker independence assumptions as till now done in the literature, new relations are given.

Standby Redundant Systems in Random Environment

AbstractReliability systems with one or two redundant standby components are studied. The systems are situated in a random environment which generates shocks according to a renewal point process. The shocks will cause a component to fail with a certain probability. Failed components are immediately repaired and the repair times are exponentially distributed. Special consideration is given to systems with cold and with warm standby components. Numerical studies are made of the effect of standby and of repair when shocks are generated by a Poisson process.

Neobiosynthesis of phosphatidylinositol and of other glycerolipids in the entire cattle retina.

The vertebrate retina comprises two different portions, a neural part and a specialized layer of photoreceptor cells. Because the former is an integral part of the central nervous system it contains a large surface of excitable membranes. Also, a very high proportion of the photoreceptor cell mass is made up of tightly folded membranes. Each portion of the retina requires polar lipids for its membranes. However, the lipid composition and metabolism of the two portions differ strikingly. This is in part an assumption since whole photoreceptor cells have not yet been isolated and direct biochemical investigations are thus not possible. However, isolated rod outer segments are currently being intensively studied. They have a high phospholipid content and are very rich in polyenoic acyl chains (Anderson, 1970; Mason et al., 1973; Daemen, 1973). Although retina homogenates and subcellular fractions display several enzymatic activities for phospholipid synthesis and breakdown the rod outer segments seem to be devoid of these pathways (Swartz & Mitchell, 1970, 1973, 1974). The temperature — and light-stimulated continuous photoreceptor membrane renewal points to an active and specialized membrane biosynthetic process in the inner segment. Moreover, Bibb & Young (1974) concluded from autoradiographic analysis that phospholipids formed from (2-3H)-glycerol are concentrated initially in the inner segments, then aggregated at the base of rod outer segments and later appear in the outer segments.KeywordsOuter SegmentPhosphatidic AcidPhotoreceptor CellPhospholipid SynthesisVertebrate RetinaThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Reliability systems in random environment

A parallel reliability system is subject to shocks which are generated by a renewal point process. The shocks cause the components to fail with certain probabilities. First we study the case when the components fail independently of each other with the same probability. For this case simple closed expressions for the Laplace-Stieltjes transform and expectation of time to system failure are derived. Then a case of dependent components is studied: the probability of failure of a component depends on the number of functioning components. Some extensions are mentioned.

Reliability systems in random environment

A parallel reliability system is subject to shocks which are generated by a renewal point process. The shocks cause the components to fail with certain probabilities. First we study the case when the components fail independently of each other with the same probability. For this case simple closed expressions for the Laplace-Stieltjes transform and expectation of time to system failure are derived. Then a case of dependent components is studied: the probability of failure of a component depends on the number of functioning components. Some extensions are mentioned.

When does a renewal, or other stationary point process, start?

Abstract It was the Swiss actuary Chr. Moser who, in lectures at Bern University at the turn of the century, gave the name “self-renewing aggregate” to what Vajda (1947) has called the “unstationary community” of lives, namely where deaths at any epoch are immediately replaced by an equivalent number of births. It was Moser too (1926) who coined the expression “steady state” for the stationary community in which the age distribution at any time follows the life table (King, 1887). With such a distinguished actuarial history, excellently summarized by Saxer (1958, Ch. IV), it behoves every actuary to know at least the definitions and modus operandi of today's so-called renewal (point), or recurrent event, processes.

Interference between independent processes

The first time independent, parallel processes consisting of two alternating renewal functions, say function zero and one, will be in phase zero together under equilibrium and non-equilibrium starting conditions is found. With function one an exponential distribution and function zero a non-lattice type, the distribution of the aforementioned time is found by taking advantage of a point of renewal. Further results are derived when both functions are exponential with the same parameter value by likening the situation to an Ehrenfest model The results are applicable to many situations. Examples taken from machine interference, reliability with redundancy, queueing at parallel stations, ‘ channel ’ interference in computer systems and communications nets are included.

The superposition of the backward and forward processes of a renewal process

A fixed sampling point O is chosen independently of a renewal process ▪ on the whole real line. The distances Y 1, Y 2, … from O to the renewal points of ▪, when they are measured either forwards or backwards in time, define a point process ▪. The process ▪ is a folding over of the past of ▪ onto its future. It is the superposition of two equilibrium renewal processes which are known to be independent only when ▪ is a Poisson process. The joint distribution of Y 1, Y 2, …, Y k is found. The marginal distribution of 2 Y k is shown to be the same as that of the distance from O to the k th following point of ▪. The intervals of ▪ are shown to have a stationarity property, and it is proved that if any pair of adjacent intervals of ▪ are independent, then ▪ is a Poisson process.

Reliability of a Repairable System with Standby Failure

This paper deals with a system in which one unit is operating online and is backed my m spares as warm standbys. There are r repair facilities. The on-line unit has an arbitrary lifetime distribution, while the spares have exponential failure time distributions. The repair time distribution is also exponential. This problem, viewed as a queuing problem, cannot be solved; but by locating a set of renewal points, we write the equations governing the states of the system and calculate the reliability and availability. Explicit results are obtained in the case of five redundant units and three repair facilities.

Thinning of Renewal Point Processes: A Flow Graph Study.

Thinning of Renewal Point Processes: A Flow Graph Study.

Book Reviews

Abstract Abstract I.Q. in the Meritocracy; R.J. Herrnstein. Boston: Little, Brown and Company, 1973. x+235 pp. $7.95. Reviewed by Bruce K. Eckland, Howabd F. Taylor Introductory Statistics with FORTRAN; Allan M. Kirch. New York: Holt, Rinehart and Winston, Inc., 1973. xv+458 pp. $11.50. Reviewed by G. P. McCabe A Textbook of Econometrics, 2nd ed.; Lawrence R. Klein. Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1973. x+436 pp. $14.50. Reviewed by Roger W. Klein Mathematical Models of Conception and Birth; Mindel C. Sheps and Jane A. Menken. Chicago: University of Chicago Press, 1973. xxiv+428 pp. $18.50. Reviewed by Joel E. Cohen Multivariate Analysis; Anant M. Kshirsagar. New York: Marcel Dekker, Inc., 1972. xiv+534 pp. $19.50. Reviewed by Christine Santini Regenerative Phenomena; J.F.C. Kingman. New York: John Wiley and Sons, Inc., 1972. xii+190 pp. $14.95. Reviewed by N.U. Prabhu An Introduction to Medical Statistics; H.O. Lancaster. New York: John Wiley and Sons, Inc., 1974. xiv+305 pp. $18.95. Reviewed by Peter A. Lachenbruch Mulricollinearity in Linear Economic Models; D. Neeleraan. Tilburg, The Netherlands: Tilburg University Press, 1973. viii+103 pp. $16.75. Reviewed by James B. Ramsey The Dependability of Behavioral Measurements: Theory of Generalizability for Scores and Profiles; Lee J. Cronbach, Goldine C. Gleser, Harinder Nanda and Nageswari Rajaratnam. New York: John Wiley and Sons, Inc., 1972. xix+410 pp. $12.95. Reviewed by Donald B. Rubin Introduction to the Theory of Statistics, 3rd ed.; Alexander M. Mood, Franklin A. Graybill and Duane C. Boes. New York: McGraw-Hill Book Company, 1974. xvi+564 pp. $12.50. Reviewed by Gordon V. Kass Thinning of Renewal Point Processes: A Flow Graph Study; Lennart Råde. Goteborg, Sweden: Mathematisk Statistik AB, 1972. 178 pp. $8.00, paperback. Reviewed by David Oakes An Introduction to Applied Macroeconomics; Edwin Kuh and Richard L. Schmalensee. New York: American Elsevier Publishing Company, Inc., 1973. v+229 pp. $13.95. Reviewed by E. Philip Howrey Foundations of Statistical Inference, A Symposium; V.P. Godambe and D.A. Sprott, Editors. Toronto: Holt, Rinehart and Winston of Canada, Ltd., 1971. viii+519 pp. $26.25. Reviewed by Judah Rosenblatt Mathematical Statistics: An Introduction Based on the Normal Distribution; Simeon M. Berman. Scranton, Pennsylvania: Intext Educational Publishers, 1971. xvi+392 pp. $12.00. Reviewed by Judah Rosenblatt Staff Reviews: Statistical Methods and Scientific Inference, 3rd ed.; Sir Ronald A. Fisher. New York: Hafner Press, 1973. xiii+180 pp. $9.95 Staff Reviews: Scientific Inference, 3rd ed.; Sir Harold Jeffreys. New York: Cambridge University Press, 1973. viii+273 pp. $16.50 Staff Reviews: Business Statistics: A First Course; John E. Freund and Benjamin M. Perles. Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1974. vii+359 pp. $10.95 Staff Reviews: Statistics: An Intuitive Approach, 3rd ed.; George H. Weinberg and John A. Schumaker. Monterey: Brooks/Cole Publishing Co., 1974. xv+392 pp. $9.95 (study guide by Freeman F. Elzey, $3.95, paperback) Staff Reviews: Statistics for Social Scientists: A Coordinated Learning System; Frank J. Kohout. New York: John Wiley and Sons, Inc., 1974. xi+452 pp. $9.95

Renewal processes with several types of renewal points

Renewal processes with several types of renewal points

Limit theorems for thinning of renewal point processes

Limit theorems for the thinning of renewal point processes according to two different schemes are studied. In the first scheme when a point is retained a random number of succeeding points are deleted. According to the second scheme a random number of points are deleted by an inhibitory Poisson process.