The numerics of Premium Bonds

2016 ◽  
Vol 9 (3) ◽  
pp. 14-33
Author(s):  
Dirk Tasche
Keyword(s):  
Probability Distribution ◽  
Fourier Transforms ◽  
Value Distribution ◽  
Hypergeometric Distribution ◽  
Exact Calculation ◽  
Single Bond ◽  
Panjer Recursion ◽  
The Uk ◽  
Interest Payments ◽  
Multivariate Hypergeometric Distribution

Premium Bonds sold by the UK National Savings and Investments (NS&I) agency are the possibly most popular example of lottery bonds. Premium Bonds holders renounce interest payments but instead participate in a lottery which distributes the equivalent of aggregate interest payments among them. While the random mechanism used in the lottery is well-documented the details of how to determine the probability distribution of a single bond holder's lottery prizes seem to be less well-known. We observe that the lottery prizes distribution is a multivariate hypergeometric distribution and discuss how to exactly calculate its probability masses as well as how to approximate the distribution by means of the Panjer recursion and Fourier transforms. We find that there are good reasons to prefer the approximations based on Panjer recursionor Fourier transforms to exact calculation of the lottery prize value distribution.

A non-central multivariate hypergeometric distribution arising from biased sampling with application to selective predation

1976 ◽  
Vol 13 (04) ◽  
pp. 795-797 ◽  
Author(s):  
Jean Chesson
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Hypergeometric Distribution ◽  
Biased Sampling ◽  
Selective Predation ◽  
Multivariate Hypergeometric Distribution

Selective predation is an example of biased sampling which gives rise to a non-central multivariate hypergeometric distribution. The probability distribution function of this distribution is derived.

A non-central multivariate hypergeometric distribution arising from biased sampling with application to selective predation

1976 ◽  
Vol 13 (4) ◽  
pp. 795-797 ◽  
Author(s):  
Jean Chesson
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Hypergeometric Distribution ◽  
Biased Sampling ◽  
Selective Predation ◽  
Multivariate Hypergeometric Distribution

Selective predation is an example of biased sampling which gives rise to a non-central multivariate hypergeometric distribution. The probability distribution function of this distribution is derived.

Certain Fourier Transforms of Distributions

1951 ◽  
Vol 3 ◽  
pp. 140-144 ◽  
Author(s):  
Eugene Lukacs ◽  
Otto Szasz
Keyword(s):  
Probability Distribution ◽  
Characteristic Function ◽  
Fourier Transforms ◽  
Probability Distributions ◽  
Distribution Functions ◽  
Characteristic Functions

Fourier transforms of distribution functions are frequently studied in the theory of probability. In this connection they are called characteristic functions of probability distributions. It is often of interest to decide whether a given function φ(t) can be the characteristic function of a probability distribution, that is, whether it admits the representation

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