Remarks on a model of competitive bidding for employment

1983 ◽  
Vol 20 (02) ◽  
pp. 349-357
Author(s):  
Anthony G. Pakes
Keyword(s):  
Random Number ◽  
Random Variable ◽  
Competitive Bidding ◽  
Complete Analysis ◽  
Income Distributions ◽  
Present Generation

Arnold and Laguna introduced a model for income distributions in which the income of the present generation of individuals has the same distribution as the minimum of a random number Nn of independent copies of some random variable and {Nn } is independent. The present paper gives a fairly complete analysis of this model and a number of extensions of it.

Remarks on a model of competitive bidding for employment

1983 ◽  
Vol 20 (2) ◽  
pp. 349-357 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Random Number ◽  
Random Variable ◽  
Competitive Bidding ◽  
Complete Analysis ◽  
Income Distributions ◽  
Present Generation

Arnold and Laguna introduced a model for income distributions in which the income of the present generation of individuals has the same distribution as the minimum of a random number Nn of independent copies of some random variable and {Nn} is independent. The present paper gives a fairly complete analysis of this model and a number of extensions of it.

scholarly journals Natural Test for Random Numbers Generator Based on Exponential Distribution

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 920 ◽  
Author(s):  
Tanackov ◽  
Sinani ◽  
Stanković ◽  
Bogdanović ◽  
Stević ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Mathematical Expectation ◽  
Random Number ◽  
Random Variable ◽  
Random Numbers ◽  
The Third ◽  
Atmospheric Noise ◽  
Constant E ◽  
Fourth Series ◽  
Natural Test

We will prove that when uniformly distributed random numbers are sorted by value, their successive differences are a exponentially distributed random variable Ex(λ). For a set of n random numbers, the parameters of mathematical expectation and standard deviation is λ =n−1. The theorem was verified on four series of 200 sets of 101 random numbers each. The first series was obtained on the basis of decimals of the constant e=2.718281…, the second on the decimals of the constant π =3.141592…, the third on a Pseudo Random Number generated from Excel function RAND, and the fourth series of True Random Number generated from atmospheric noise. The obtained results confirm the application of the derived theorem in practice.

Supercritical age-dependent branching processes with immigration

1974 ◽  
Vol 11 (4) ◽  
pp. 695-702 ◽  
Author(s):  
K. B. Athreya ◽  
P. R. Parthasarathy ◽  
G. Sankaranarayanan
Keyword(s):  
Branching Process ◽  
Random Number ◽  
Branching Processes ◽  
Life Time ◽  
Random Variable ◽  
One Dimensional ◽  
Malthusian Parameter ◽  
Age Dependent ◽  
Branching Process With Immigration ◽  
Mutually Independent

A branching process with immigration of the following type is considered. For every i, a random number Ni of particles join the system at time . These particles evolve according to a one-dimensional age-dependent branching process with offspring p.g.f. and life time distribution G(t). Assume . Then it is shown that Z(t) e–αt converges in distribution to an extended real-valued random variable Y where a is the Malthusian parameter. We do not require the sequences {τi} or {Ni} to be independent or identically distributed or even mutually independent.

scholarly journals Theorems on large deviations for the sum of random number of summands

2010 ◽  
Vol 51 ◽  
Author(s):  
Aurelija Kasparavičiūtė ◽  
Leonas Saulis
Keyword(s):  
Large Deviations ◽  
Rate Of Convergence ◽  
Random Number ◽  
Normal Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Compound Process ◽  
Independent Identically Distributed

In this paper, we present the rate of convergence of normal approximation and the theorem on large deviations for a compound process Zt = \sumNt i=1 t aiXi, where Z0 = 0 and ai > 0, of weighted independent identically distributed random variables Xi, i = 1, 2, . . . with  mean EXi = µ and variance DXi = σ2 > 0. It is assumed that Nt is a non-negative integervalued random variable, which depends on t > 0 and is independent of Xi, i = 1, 2, . . . .

scholarly journals Optimistic Changes in the Characters of Shashi Deshpande’s in A Matter of Time

2021 ◽  
Vol 9 (5) ◽  
pp. 72-80
Author(s):  
M. Saraswathy
Keyword(s):  
Mental Illness ◽  
Human Life ◽  
Modern Society ◽  
Complete Analysis ◽  
Human Beings ◽  
Present Generation ◽  
Negative Thoughts ◽  
The World ◽  
Thinking Process ◽  
Shashi Deshpande

Shashi Deshpande focuses the need of human beings of present generation to be optimistic in the fast moving planetary as human life across the world is turning bleak time and again. In modern society, people fail to train their minds to be positive, they intentionally or unintentionally give space for emotions and thoughts to torture their thoughts perhaps and that leads to mental illness and carries malicious reflection in individuals, families and societies. Shashi Deshpande does a complete analysis on the rational thinking process of human beings to create happiness and to experience the power of one’s creation in this cosmic. Through her characters, Shashi Deshpande makes the readers understand that to enhance and empower their role in life, they must learn to unlearn negative thoughts and fill their minds with positive thoughts.

scholarly journals Normal approximation for sum of random number of summands

2021 ◽  
Vol 47 ◽  
Author(s):  
Leonas Saulis ◽  
Dovilė Deltuvienė
Keyword(s):  
Large Deviations ◽  
Random Number ◽  
Normal Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Negative Integer

Normal aproximationof sum Zt =ΣNti=1Xi of i.i.d. random variables (r.v.) Xi , i = 1, 2, . . . with mean EXi = μ and variance DXi = σ2 > 0 is analyzed taking into consideration large deviations. Here Nt is non-negative integer-valued random variable, which depends on t , but not depends at Xi , i = 1, 2, . . ..

Random coverage of a circle with applications to a shadowing problem

1982 ◽  
Vol 19 (03) ◽  
pp. 562-577 ◽  
Author(s):  
M. Yadin ◽  
S. Zacks
Keyword(s):  
Random Number ◽  
Random Variable ◽  
Point Of View ◽  
Numerical Determination ◽  
Coverage Problem ◽  
Random Location

The coverage problem on the circle is considered from the shadowing process point of view. A random number of shadow arcs are distributed on a circle. The length of each arc is a random variable which depends on the random diameter of a shadowing disk and its random location. Formulae are derived for the numerical determination of the moments of the measure of vacancy of arcs on the circle, for a special example. An approximation to the distribution of the measure of vacancy is also provided.

scholarly journals Asymptotics for randomly reinforced urns with random barriers

2016 ◽  
Vol 53 (4) ◽  
pp. 1206-1220
Author(s):  
Patrizia Berti ◽  
Irene Crimaldi ◽  
Luca Pratelli ◽  
Pietro Rigo
Keyword(s):  
Conditional Distribution ◽  
Random Number ◽  
Random Variable ◽  
Conditional Convergence ◽  
Mild Conditions ◽  
The Past ◽  
Random Variance

Abstract An urn contains black and red balls. Let Zn be the proportion of black balls at time n and 0≤L<U≤1 random barriers. At each time n, a ball bn is drawn. If bn is black and Zn-1<U, then bn is replaced together with a random number Bn of black balls. If bn is red and Zn-1>L, then bn is replaced together with a random number Rn of red balls. Otherwise, no additional balls are added, and bn alone is replaced. In this paper we assume that Rn=Bn. Then, under mild conditions, it is shown that Zn→a.s.Z for some random variable Z, and Dn≔√n(Zn-Z)→𝒩(0,σ2) conditionally almost surely (a.s.), where σ2 is a certain random variance. Almost sure conditional convergence means that ℙ(Dn∈⋅|𝒢n)→w 𝒩(0,σ2) a.s., where ℙ(Dn∈⋅|𝒢n) is a regular version of the conditional distribution of Dn given the past 𝒢n. Thus, in particular, one obtains Dn→𝒩(0,σ2) stably. It is also shown that L<Z<U a.s. and Z has nonatomic distribution.

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