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Manuals/calci/NEGBINOMDIST (view source)
Revision as of 11:15, 28 November 2013
, 11:15, 28 November 2013→Description
*This function gives the Negative Binomial Distribution.
*This function gives the Negative Binomial Distribution.
*Negative Binomial Distribution is the discrete probability distribution with the fixed probability of success.
*Negative Binomial Distribution is the discrete probability distribution with the fixed probability of success.
*It is also called Pascal distribution.
*It is also called Pascal Distribution.
This is the statistical experiment with the following conditions:
This is the statistical experiment with the following conditions:
This experiment consists of a sequence of independent trials.
This experiment consists of a sequence of independent trials.
The probability of success is constant from trial to trial
The probability of success is constant from trial to trial
The trials are independent; ie, the outcome on one trial does not affect the outcome on other trials.
The trials are independent; ie, the outcome on one trial does not affect the outcome on other trials.
The experiment continues until <math>r</math> successes are observed, where <math>r</math> is a specified positive integer.
The experiment continues until <math>r</math> the successes is obtained, where <math>r</math> is a specified positive integer.
*The random variable of <math>x</math> = the number of failures that precede the <math>r^{th}</math> success;
*The random variable <math>x</math> = the number of failures that precede the <math>r^{th}</math> success;
*<math>x</math> is called a Negative Binomial Random variable because, in contrast to the
*<math>x</math> 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.
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:
*Then probability mass function of the negative binomial distribution is
nb(x;r,p)=(x+r-1 p^r (1-p)^x r-1)
:<math>nb(x;r,p)=(x+r-1 p^r (1-p)^x r-1)</math>
*For example: If a fair coin is tossed repeatedly, what is the probability that at least 10 tosses are required.
*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
to obtain heads 8 times