scholarly journals Derivation of the mean highest reversal floor and expected number of stops in lift systems

1979 ◽  
Vol 3 (4) ◽  
pp. 275-279 ◽  
Author(s):  
N.A. Alexandris ◽  
G.C. Barney ◽  
C.J. Harris
Keyword(s):  
Expected Number ◽  
The Mean

Distribution of the number of alleles in multigene families

1992 ◽  
Vol 29 (04) ◽  
pp. 759-769
Author(s):  
R. C. Griffiths
Keyword(s):  
Stochastic Model ◽  
Gene Conversion ◽  
Lower Bounds ◽  
Multigene Families ◽  
Expected Number ◽  
Allele Type ◽  
The Mean

The distribution of the number of alleles in samples from r chromosomes is studied. The stochastic model used includes gene conversion within chromosomes and mutation at loci on the chromosomes. A method is described for simulating the distribution of alleles and an algorithm given for computing lower bounds for the mean number of alleles. A formula is derived for the expected number of samples from r chromosomes which contain the allele type of a locus chosen at random.

scholarly journals Some Problems Connected with the Calculation of Stop Loss Premiums for Large Portfolios

1967 ◽  
Vol 4 (2) ◽  
pp. 170-174 ◽  
Author(s):  
Fredrik Esscher
Keyword(s):  
Distribution Function ◽  
Expected Number ◽  
Limit Values ◽  
Empirical Determination ◽  
The Mean ◽  
Premium Rates ◽  
Image Position ◽  
Stop Loss ◽  
The Given

When experience is insufficient to permit a direct empirical determination of the premium rates of a Stop Loss Cover, we have to fall back upon mathematical models from the theory of probability—especially the collective theory of risk—and upon such assumptions as may be considered reasonable.The paper deals with some problems connected with such calculations of Stop Loss premiums for a portfolio consisting of non-life insurances. The portfolio was so large that the values of the premium rates and other quantities required could be approximated by their limit values, obtained according to theory when the expected number of claims tends to infinity.The calculations were based on the following assumptions.Let F(x, t) denote the probability that the total amount of claims paid during a given period of time is ≤ x when the expected number of claims during the same period increases from o to t. The net premium II (x, t) for a Stop Loss reinsurance covering the amount by which the total amount of claims paid during this period may exceed x, is defined by the formula and the variance of the amount (z—x) to be paid on account of the Stop Loss Cover, by the formula As to the distribution function F(x, t) it is assumed that wherePn(t) is the probability that n claims have occurred during the given period, when the expected number of claims increases from o to t,V(x) is the distribution function of the claims, giving the conditioned probability that the amount of a claim is ≤ x when it is known that a claim has occurred, andVn*(x) is the nth convolution of the function V(x) with itself.V(x) is supposed to be normalized so that the mean = I.

scholarly journals Bounds for the Asymptotic Growth Rate of an Age-Dependent Branching Process

1969 ◽  
Vol 10 (1-2) ◽  
pp. 231-235 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Growth Rate ◽  
Population Size ◽  
Branching Process ◽  
Expected Number ◽  
Lattice Distribution ◽  
Asymptotic Growth ◽  
Age Dependent ◽  
The Mean ◽  
Image Position ◽  
Asymptotic Growth Rate

Let M(t) denote the mean population size at time t (conditional on a single ancestor of age zero at time zero) of a branching process in which the distribution of the lifetime T of an individual is given by Pr {T≦t} =G(t), and in which each individual gives rise (at death) to an expected number A of offspring (1λ A λ ∞). expected number A of offspring (1 < A ∞). Then it is well-known (Harris [1], p. 143) that, provided G(O+)-G(O-) 0 and G is not a lattice distribution, M(t) is given asymptotically by where c is the unique positive value of p satisfying the equation .

Branching diffusion processes in population genetics

1976 ◽  
Vol 8 (04) ◽  
pp. 659-689 ◽  
Author(s):  
Stanley Sawyer
Keyword(s):  
Random Fields ◽  
Diffusion Processes ◽  
Migration Process ◽  
Expected Number ◽  
Explicit Formulas ◽  
Limit Laws ◽  
The Mean ◽  
Relationship Of ◽  
Number Of Individuals ◽  
Neutral Mutation Rate

A branching random field is considered as a model of either of two situations in genetics in which migration or dispersion plays a role. Specifically we consider the expected number of individualsNAin a (geographical) setAat timet, the covariance ofNAandNBfor two setsA, B, and the probabilityI(x, y, u) that two individuals found at locationsx, yat timetare of the same genetic type if the population is subject to a selectively neutral mutation rateu.The last also leads to limit laws for the average degree of relationship of individuals in various types of branching random fields. We also find the equations that the mean and bivariate densities satisfy, and explicit formulas when the underlying migration process is Brownian motion.

The convexity of the mean queue size of the M/M/c queue with respect to the traffic intensity

1983 ◽  
Vol 20 (4) ◽  
pp. 916-919 ◽  
Author(s):  
W. Grassmann
Keyword(s):  
Second Derivative ◽  
Traffic Intensity ◽  
Queue Size ◽  
Expected Number ◽  
The Mean

In this paper, we show that the expected number in an M/M/c queue is convex with respect to the traffic intensity. The proof is conducted by expressing the second derivative of the expected queue size as the sum of non-negative terms.

Estimating the Mean Number of Renewals By Simulation

1989 ◽  
Vol 3 (3) ◽  
pp. 319-321 ◽  
Author(s):  
Sheldon M. Ross
Keyword(s):  
Renewal Process ◽  
Conditional Expectation ◽  
Expected Number ◽  
Control Variates ◽  
The Mean

An estimator, based on a simulation, is given for the expected number of events by time t of a renewal process. The estimator is obtained by combining the techniques of control variates and conditional expectation.

A Mathematical Model for Recurrent Twinning

1990 ◽  
Vol 39 (3) ◽  
pp. 307-316 ◽  
Author(s):  
J.O. Fellman ◽  
A.W. Eriksson
Keyword(s):  
Temporal Variations ◽  
Likelihood Method ◽  
Demographic Information ◽  
Poor Agreement ◽  
Expected Number ◽  
Sibship Size ◽  
Considerable Excess ◽  
The Mean ◽  
Crude Estimate ◽  
Good Agreement

AbstractIn an attempt to improve our understanding of the factors that affect human twinning, we further developed the models given by Hellin (1895) and Peller (1946). The connection between these models and our own model (“Fellman's law”) were studied. These attempts have resulted in a more general model, which was then applied to data from Åland Islands (1750-1939), Nîmes (1790-1875), Stuttgart (about 1790-1900) and Utah (1850-1900). The product of the mean sibship size and the total twinning rate can be considered as a crude estimate of the expected number of sets of twins in a sibship. The same can be said about the twinning parameter in our model. These estimates are in good agreement. If we consider twinning data only, we obtain the geometric distribution, and log (Nk), where Nk is the number of mothers with k twin maternities, is a linear function of the number of recurrences. Graphically, this property can easily be checked. For sibships containing three or more sets of twins, all four populations show higher values than expected, particularly the populations from Stuttgart and Utah, which data also show poor agreement according to a χ2-test. A more exact model would demand more detailed demographic information, such as distribution of sibship sizes, age-specific twinning rates and temporal variations in twinning.The osberved number of mothers in Åland with several recurrences of multiple maternities shows a considerable excess over the expected number as predicted by Peller's rule. The parameters in our model can be estimated by the maximum likelihood method and the obtained model fits the data better then Peller's model.

The convexity of the mean queue size of the M/M/c queue with respect to the traffic intensity

1983 ◽  
Vol 20 (04) ◽  
pp. 916-919 ◽  
Author(s):  
W. Grassmann
Keyword(s):  
Second Derivative ◽  
Traffic Intensity ◽  
Queue Size ◽  
Expected Number ◽  
The Mean

In this paper, we show that the expected number in an M/M/c queue is convex with respect to the traffic intensity. The proof is conducted by expressing the second derivative of the expected queue size as the sum of non-negative terms.

scholarly journals Zeros of an algebraic polynomial with nonequal means random coefficients

2004 ◽  
Vol 2004 (63) ◽  
pp. 3389-3395
Author(s):  
K. Farahmand ◽  
P. Flood
Keyword(s):  
Algebraic Polynomial ◽  
Asymptotic Estimate ◽  
Random Variables ◽  
Random Coefficients ◽  
Random Polynomial ◽  
Expected Number ◽  
Real Zeros ◽  
Number Of Real Zeros ◽  
The Mean

This paper provides an asymptotic estimate for the expected number of real zeros of a random algebraic polynomiala0+a1x+a2x2+⋯+an−1xn−1. The coefficientsaj(j=0,1,2,…,n−1)are assumed to be independent normal random variables with nonidentical means. Previous results are mainly for identically distributed coefficients. Our result remains valid when the means of the coefficients are divided into many groups of equal sizes. We show that the behaviour of the random polynomial is dictated by the mean of the first group of the coefficients in the interval(−1,1)and the mean of the last group in(−∞,−1)∪(1,∞).

Distribution of the number of alleles in multigene families

1992 ◽  
Vol 29 (4) ◽  
pp. 759-769 ◽  
Author(s):  
R. C. Griffiths
Keyword(s):  
Stochastic Model ◽  
Gene Conversion ◽  
Lower Bounds ◽  
Multigene Families ◽  
Expected Number ◽  
Allele Type ◽  
The Mean

The distribution of the number of alleles in samples from r chromosomes is studied. The stochastic model used includes gene conversion within chromosomes and mutation at loci on the chromosomes. A method is described for simulating the distribution of alleles and an algorithm given for computing lower bounds for the mean number of alleles.A formula is derived for the expected number of samples from r chromosomes which contain the allele type of a locus chosen at random.

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