Negative Binomial Question

I keep on seeing different versions of the same formula of the NB. For example look at the mean and variance here and here. One might say it's easy if you change the letters, but everywhere p means success and q failure.

All I see is p/q = q/p , which is absurd.

Is there something I don't understand?

(edited 11 years ago)

Reply 1

smd4std

yes there is something that you don't understand.

Reply 2

erniiee

13

Original post by smd4std

yes there is something that you don't understand.

Haha the pic in your sig is so appropriate for your post, and this thread in general :lol:

Reply 3

ted25

OP

Original post by smd4std

yes there is something that you don't understand.

lol. Do you know what is it?

Reply 4

TenOfThem

18

Original post by ted25

I keep on seeing different versions of the same formula of the NB. For example look at the mean and variance here and here. One might say it's easy if you change the letters, but everywhere p means success and q failure.

All I see is p/q = q/p , which is absurd.

Is there something I don't understand?

Are you confused by the fact that

^nC_p = ^nC_q

Reply 5

smd4std

Original post by ted25

lol. Do you know what is it?

what's important here is that you're confused about something

Reply 6

ted25

OP

Original post by TenOfThem

Are you confused by the fact that

^nC_p = ^nC_q

???

Reply 7

ted25

OP

Did I get an explanation?

Reply 8

shamika

16

I think Wikipedia is wrong. What is your definition of the probability mass function for the negative Binomial? A further source of confusion is that there are two different types of negative Binomial distributions;

one has support

x=k,x=k+1,...

and the other (the one I think you're after) having support

x=0,1,...

.

The mass function I use is

f(x)=\frac{\Gamma(k+x)}{\Gamma(x+1)\Gamma(k)}p^k(1-p)^x

. If that's the same as yours, Wolfram has it right.

You should be able to derive the mean yourself - work out what the moment generating function is, and use that to get the mean.

Reply 9

ted25

OP

They are counting till "r" failures, I'm counting till "r" successes. The mean and variance @ wiki is counting till r failures and @ wolfram till r successes? :confused:

Also wiki is counting the success till r failures. I though that NB counts the trials. So we've got 4(!) NBs.

NB1 the number of failures till r successes
NB2 the number of success till r failures
NB3 the number of trials till r successes
NB4 the number of trials till r failures

:mad:

(edited 11 years ago)

Reply 10

shamika

16

Original post by ted25

They are counting till "r" failures, I'm counting till "r" successes. The mean and variance @ wiki is counting till r failures and @ wolfram till r successes? :confused:

Oh - well then that explains it. Both formulae (the Wiki and the Mathworld one) are consistent then

Negative Binomial Question

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