Tail Bounds for Occupancy Problems, 1995; Kamath, Motwani, Palem, Spirakis

2011 ◽  
Keyword(s):  
Occupancy Problems

A central limit theorem for exchangeable variates with geometric applications

1973 ◽  
Vol 10 (4) ◽  
pp. 837-846 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Asymptotic Normality ◽  
Central Limit ◽  
Random Variables ◽  
Multinomial Distribution ◽  
Sum Of Random Variables ◽  
Th Cell ◽  
Occupancy Problems

A central limit theorem is proved for the sum of random variables Xr all having the same form of distribution and each of which depends on a parameter which is the number occurring in the rth cell of a multinomial distribution with equal probabilities in N cells and a total n, where nN–1 tends to a non-zero constant. This result is used to prove the asymptotic normality of the distribution of the fractional volume of a large cube which is not covered by N interpenetrating spheres whose centres are at random, and for which NV–1 tends to a non-zero constant. The same theorem can be used to prove asymptotic normality for a large number of occupancy problems.

Limit theorems for some sequential occupancy problems

1983 ◽  
Vol 20 (03) ◽  
pp. 545-553 ◽  
Author(s):  
Svante Janson
Keyword(s):  
Limit Theorems ◽  
Random Variables ◽  
Asymptotic Results ◽  
Occupancy Problems ◽  
Number Of Cells

Consider n cells into which balls are thrown at random until all but m cells contain at least l + 1 balls each. Asymptotic results when n →∞, m and l held fixed, are given for the number of cells containing exactly k balls and for related random variables.

scholarly journals Convergence Properties in Certain Occupancy Problems Including the Karlin-Rouault Law

2011 ◽  
Vol 48 (4) ◽  
pp. 1095-1113 ◽  
Author(s):  
Estáte V. Khmaladze
Keyword(s):  
Asymptotic Analysis ◽  
Sample Size ◽  
Asymptotic Expression ◽  
Convergence Properties ◽  
Natural Conditions ◽  
Asymptotic Results ◽  
Joint Behaviour ◽  
Occupancy Problems

Let x denote a vector of length q consisting of 0s and 1s. It can be interpreted as an ‘opinion’ comprised of a particular set of responses to a questionnaire consisting of q questions, each having {0, 1}-valued answers. Suppose that the questionnaire is answered by n individuals, thus providing n ‘opinions’. Probabilities of the answer 1 to each question can be, basically, arbitrary and different for different questions. Out of the 2q different opinions, what number, μn, would one expect to see in the sample? How many of these opinions, μn(k), will occur exactly k times? In this paper we give an asymptotic expression for μn / 2q and the limit for the ratios μn(k)/μn, when the number of questions q increases along with the sample size n so that n = λ2q, where λ is a constant. Let p(x) denote the probability of opinion x. The key step in proving the asymptotic results as indicated is the asymptotic analysis of the joint behaviour of the intensities np(x). For example, one of our results states that, under certain natural conditions, for any z > 0, ∑1{np(x) > z} = dnz−u, dn = o(2q).

scholarly journals Outreach of Pro-poor Housing Programs and Projects: Is it sustained?

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Gowthami Sai Dubagunta ◽  
Sejal Patel
Keyword(s):  
Affordable Housing ◽  
User Satisfaction ◽  
Urban Poor ◽  
Quantitative Research ◽  
Free Market ◽  
Secondary Data ◽  
Housing Supply ◽  
Formal Sector ◽  
Bottom Of Pyramid ◽  
Occupancy Problems

Affordable housing for urban poor is one among the hot button issues among all policy makers and planners in countries of global south.  Grand schemes with extravagant promises in the formal sector and gigantic hope for informal sector, to capture the opportunity at bottom of pyramid, are simultaneously trying to curb the problem of affordable housing shortage for urban poor. Even though private sector does not purposely seek to cater housing for lower income sections, yet large quantum of investment have been witnessed in housing for the urban poor. It is well known that in a free market tussle, the highest bidder is always the winner.  This has been a major reason for creation of artificial shortage of housing for poor. And the scenario is worse in case of public housing, where, half of the units are either left purposeless or used by ineligible users, largely due to risk of impoverishment and improper post occupancy vigilance. The magnitude of post occupancy problems being unexplored, the objective of paper pertains to looks at the challenges and issues in sustaining targeted outreach to intended beneficiaries in housing supply models for urban poor. The paper elaborates distinct challenges through three housing supply models in Ahmedabad, India. The models are Rehabilitation Housing, Subsidized Housing by government and market provided Housing. The method is mixed method i.e. qualitative and quantitative research using primary and secondary data sources. The critical analysis of effective outreach is carried by studying policy rhetoric in each of the models to on ground veracity in the post occupancy stage of model by assessing end user satisfaction in each model.

A unified approach to limit theorems for urn models

1979 ◽  
Vol 16 (01) ◽  
pp. 154-162 ◽  
Author(s):  
Lars Holst
Keyword(s):  
Limit Theorem ◽  
Characteristic Function ◽  
Negative Binomial Distribution ◽  
Limit Theorems ◽  
Negative Binomial ◽  
Random Variable ◽  
Unified Approach ◽  
Special Cases ◽  
Occupancy Problems ◽  
General Method

An urn contains A balls of each of N colours. At random n balls are drawn in succession without replacement, with replacement or with replacement together with S new balls of the same colour. Let Xk be the number of drawn balls having colour k, k = 1, …, N. For a given function f the characteristic function of the random variable ZM = f(X 1)+ … + f(XM ), M ≦ N, is derived. A limit theorem for ZM when M, N, n → ∞is proved by a general method. The theorem covers many special cases discussed separately in the literature. As applications of the theorem limit distributions are obtained for some occupancy problems and for dispersion statistics for the binomial, Poisson and negative-binomial distribution.

scholarly journals Multidimensional occupancy problems with Poisson randomization

1984 ◽  
Vol 104 (2) ◽  
pp. 526-536
Author(s):  
John F Buoncristiani ◽  
Mauro Cerasoli
Keyword(s):  
Occupancy Problems
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