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From |
Steven Samuels <sjhsamuels@earthlink.net> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: probability mass function for a binomial distribution |

Date |
Sun, 29 Jun 2008 13:04:44 -0400 |

I agree with Nick's advice to construct the functions on first principles whenever possible.

Interestingly, Carlo has discovered the apparently undocumented "survival' function Binomial(k,n,p) equal to P(X>=k), whereas the documented function binomial(k,n,p) is P(X<=k). Here is a version of Carlo's program with a correction for k= 20.

-Steve

/*---------------------------begin example-------------------------*/

drop _all

clear

set obs 21

g id=_n-1

g n=20

g k=_n-1

g p=.2

g double Binomial=Binomial( n, k, p)

g double PMF_Binomial=Binomial[_n]- Binomial[_n+1] in 1/20

replace PMF_Binomial=Binomial[_n] in 21 //Correction

g double PMF2 = 0.2^k * 0.8^(20 - k) * comb(20, k)

list id n k p Binomial binomial PMF*

/*--------------------------end example----------------------------*/

On Jun 29, 2008, at 11:26 AM, Nick Cox wrote:

What is available as a defined function shows up a trade-off problem. It

wouldn't be difficult to define a thousand functions, but then some

people might complain about the complexity of the list and the

difficulty of finding a solution.

Otherwise put, I guess the answer to Carlo's question is that Stata

users -- unlike spreadsheet users, it seems --- are paid the compliment

of knowing enough statistics to work this out from first principles:

gen double bmp = p^k * (1 - p)^(20 - k) * comb(20, k)

Note in passing two other details:

I prefer to use -double-s here.

Putting constants into variables isn't necessary:

gen double bmp = 0.2^k * 0.8^(20 - k) * comb(20, k)

In cases like this the advantage of a canned function over a one-line

solution using another canned function would be pretty small.

Nick

n.j.cox@durham.ac.uk

Carlo Lazzaro

I have probably found out the answer to my last Friday thread.

I do hope this may be useful for someone else on the list.

However, a little concern remains about the lack among Stata 9.2/SE

commands

of an in-built for calculating the (probably too trivial) probability

mass

function for a binomial distribution, which is instead available within

the

most widespread spreadsheets.

One more time, my grateful thought go out to Steve and Nick (in order of

appearance in my incoming e-mail folder) for pointing me out the

importance

of a step-by-step research in dealing with Stata troubles.

---------------------------begin example-------------------------

set obs 21

g id=_n-1

g n=20

g k=_n-1

g p=.2

g Binomial=Binomial( n, k, p)

g PMF_Binomial=1- Binomial if id==20

replace PMF_Binomial=Binomial[_n]- Binomial[_n+1] in 1/20

--------------------------end example----------------------------

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**Follow-Ups**:**RE: st: probability mass function for a binomial distribution***From:*Philip Ryan <philip.ryan@adelaide.edu.au>

**RE: st: probability mass function for a binomial distribution***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**References**:**R: st: probability mass function for a binomial distribution***From:*"Carlo Lazzaro" <carlo.lazzaro@tin.it>

**RE: st: probability mass function for a binomial distribution***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

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