Manuals/calci/NEGBINOMDIST

NEGBINOMDIST(nf,ns,ps)

• Where 'nf' is the number of failures.
• Where 'ns' is the number of successes on an individual trial
• And 'ps' is the probability of a success.

Description

This function gives the negative binomial distribution. Negative binomial ditrbution is the discrete probability distribution with the fixed probability of success. It is also called Pascal distribution. This is the statistical experiment with the following conditions:

1. This experiment consists of a sequence of independent trials.
2. Each trial represents only two results(Success or failure)
3. The probability of success is constant from trial to trial
4. The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.
5. The experiment continues until r successes are observed, where r is a specified positive integer.

• The random variable of x = the number of failures that precede the rth success;
• x is called a negative binomial random variable because, in contrast to the

binomial random variable, the number of successes is fixed and the number of trials is random.

• Then probability mass function of the negative binomial distribution is:

nb(x;r,p)=(x+r-1 p^r (1-p)^x r-1)

• For example:If a fair coin is tossed repeatedly, what is the probability that at least 10 tosses are required.

to obtain heads 8 times

• This function will give the result as error when:

1. Any argument is nonnumeric
2. If ps<0 or ps>1
3. If nf<0 or ns<1

Examples

=log 10(5)= 0.698970004
=log(55)= 1.740362689
=log(10)= 1
=log(1)= 0
=log(-10)= NaN
=log(0.25)= -0.602059991

See Also

• LN
• IMLOG10
• LOG

References

Logarithm