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

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.

Asymptotic Normality Through Factorial Cumulants and Partition Identities

In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments as do (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a new identity for ‘moments’ of partitions of numbers. The general limiting result is then used to (re-)derive asymptotic normality for several models including classical discrete distributions, occupancy problems in some generalized allocation schemes and two models related to negative multinomial distribution.

On the Joint Behavior of Types of Coupons in Generalized Coupon Collection

The ‘coupon collection problem’ refers to a class of occupancy problems in which j identical items are distributed, independently and at random, to n cells, with no restrictions on multiple occupancy. Identifying the cells as coupons, a coupon is ‘collected’ if the cell is occupied by one or more of the distributed items; thus, some coupons may never be collected, whereas others may be collected once or twice or more. We call the number of coupons collected exactly r times coupons of type r. The coupon collection model we consider is general, in that a random number of purchases occurs at each stage of collecting a large number of coupons; the sample sizes at each stage are independent and identically distributed according to a sampling distribution. The joint behavior of the various types is an intricate problem. In fact, there is a variety of joint central limit theorems (and other limit laws) that arise according to the interrelation between the mean, variance, and range of the sampling distribution, and of course the phase (how far we are in the collection processes). According to an appropriate combination of the mean of the sampling distribution and the number of available coupons, the phase is sublinear, linear, or superlinear. In the sublinear phase, the normalization that produces a Gaussian limit law for uncollected coupons can be used to obtain a multivariate central limit law for at most two other types — depending on the rates of growth of the mean and variance of the sampling distribution, we may have a joint central limit theorem between types 0 and 1, or between types 0, 1, and 2. In the linear phase we have a multivariate central limit theorem among the types 0, 1,…, k for any fixed k.

On the Joint Behavior of Types of Coupons in Generalized Coupon Collection

The ‘coupon collection problem’ refers to a class of occupancy problems in which j identical items are distributed, independently and at random, to n cells, with no restrictions on multiple occupancy. Identifying the cells as coupons, a coupon is ‘collected’ if the cell is occupied by one or more of the distributed items; thus, some coupons may never be collected, whereas others may be collected once or twice or more. We call the number of coupons collected exactly r times coupons of type r. The coupon collection model we consider is general, in that a random number of purchases occurs at each stage of collecting a large number of coupons; the sample sizes at each stage are independent and identically distributed according to a sampling distribution. The joint behavior of the various types is an intricate problem. In fact, there is a variety of joint central limit theorems (and other limit laws) that arise according to the interrelation between the mean, variance, and range of the sampling distribution, and of course the phase (how far we are in the collection processes). According to an appropriate combination of the mean of the sampling distribution and the number of available coupons, the phase is sublinear, linear, or superlinear. In the sublinear phase, the normalization that produces a Gaussian limit law for uncollected coupons can be used to obtain a multivariate central limit law for at most two other types — depending on the rates of growth of the mean and variance of the sampling distribution, we may have a joint central limit theorem between types 0 and 1, or between types 0, 1, and 2. In the linear phase we have a multivariate central limit theorem among the types 0, 1,…, k for any fixed k.

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

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).

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

Letxdenote a vector of lengthqconsisting of 0s and 1s. It can be interpreted as an ‘opinion’ comprised of a particular set of responses to a questionnaire consisting ofqquestions, each having {0, 1}-valued answers. Suppose that the questionnaire is answered bynindividuals, thus providingn‘opinions’. Probabilities of the answer 1 to each question can be, basically, arbitrary and different for different questions. Out of the 2qdifferent opinions, what number, μn, would one expect to see in the sample? How many of these opinions, μn(k), will occur exactlyktimes? In this paper we give an asymptotic expression for μn/ 2qand the limit for the ratios μn(k)/μn, when the number of questionsqincreases along with the sample sizenso thatn= λ2q, where λ is a constant. Letp(x) denote the probability of opinionx. The key step in proving the asymptotic results as indicated is the asymptotic analysis of the joint behaviour of the intensitiesnp(x). For example, one of our results states that, under certain natural conditions, for anyz> 0, ∑1{np(x) >z}=dnz−u,dn=o(2q).