Showing posts with label Distributions. Show all posts
Showing posts with label Distributions. Show all posts

Saturday, March 27, 2010

Binomial Probability Distributions with Microsoft Excel


Image : http://www.flickr.com


A binomial distribution describes the outcome of a multi-step experiment, consisting of
n identical trials, where each trial ends in either a success or a failure and the probability of
a success p does not change from trial to trial. This useful statistical analysis can be performed relatively easily using Microsoft Excel using the Excel BINOMDIST, CRITBINOM and NEGBINOMDIST functions.

Note, however, that when making binomial probability calculations, the trials must also be independent so that success in one trial does not affect the probability of success in another trial. The binomial random variable x is the number of successes observed in n trials.

If samples are not replaced, and therefore the outcome of one trial changes the probability of success in another trial, you need to use the hypergeometric probability distribution Excel function.

Using Excel's BINOMDIST Function

For example, if you flip a coin n times and "heads" is called a success, then the random variable
x would be the number of heads observed in n flips. It could take the values 1,2,3,...,n with different probabilities.

The BINOMDIST function uses the following syntax:

=BINOMDIST(x,n,p,cumulative)

If you want to find the probability of exactly x successes, enter FALSE as the fourth (cumulative) argument. If you want to find the probability of x or fewer successes, enter TRUE as the fourth argument.

For example, if you were to flip a fair coin 20 times and wanted to find the probability of it turning up "heads" exactly 10 times, the function looks like this:

=BINOMDIST(10,20,0.5,FALSE)

The function returns the value 0.176197052. If you wanted to find the probability of getting
10 or fewer heads, you replace the FALSE with TRUE, and the function returns the value 0.588098526.

Using Excel's CRITBINOM Function

The acceptance criterion function, CRITBINOM, is used for quality control of a production process. You use this function to find the maximum number of defective items that a person can find in a lot and still allow acceptance of the lot. Inspectors should accept the lot if they find this number or fewer defective items and reject the lot if they find more defective items.

To determine the acceptance criterion, you need to know the number of items in the lot, the probability of accepting each item, and the producer's allowable risk (alpha) for rejecting an acceptable lot.

The CRITBINOM function uses the following syntax:

=CRITBINOM (trials, probability_s, alpha)

where trials is the number of trials, probability's is the probability of a success on each trial,
and alpha is the criterion value. Probability's and alpha are both between 0 and 1.

Using Excel's NEGBINOMDIST Function

If the number of successes is fixed in a binomial distribution and you want to find the number of trials, use the NEGBINOMDIST function. This function returns the probability that there will be a certain number of failures before the threshold number of successes, given the constant probability of a success.

For example, if you need to find 20 straight 2 by 4s from a stack, and you know the probability that a board in the stack is straight is 0.2 (20%), you can use the NEGBINOMDIST to find that there is about a 2% probability that you will reject 75 boards before finding all 20 straight ones.

The NEGBINOMDIST function uses the following syntax:

=NEGBINOMDIST (number failures, number successes, probability of success)

For this example, the function looks like this:

=negbinomdist (75, 20, 0.2)

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Wednesday, March 24, 2010

Binomial Probability Distributions with Microsoft Excel


Image : http://www.flickr.com


A binomial distribution describes the outcome of a multi-step experiment, consisting of
n identical trials, where each trial ends in either a success or a failure and the probability of
a success p does not change from trial to trial. This useful statistical analysis can be performed relatively easily using Microsoft Excel using the Excel BINOMDIST, CRITBINOM and NEGBINOMDIST functions.

Note, however, that when making binomial probability calculations, the trials must also be independent so that success in one trial does not affect the probability of success in another trial. The binomial random variable x is the number of successes observed in n trials.

If samples are not replaced, and therefore the outcome of one trial changes the probability of success in another trial, you need to use the hypergeometric probability distribution Excel function.

Using Excel's BINOMDIST Function

For example, if you flip a coin n times and "heads" is called a success, then the random variable
x would be the number of heads observed in n flips. It could take the values 1,2,3,...,n with different probabilities.

The BINOMDIST function uses the following syntax:

=BINOMDIST(x,n,p,cumulative)

If you want to find the probability of exactly x successes, enter FALSE as the fourth (cumulative) argument. If you want to find the probability of x or fewer successes, enter TRUE as the fourth argument.

For example, if you were to flip a fair coin 20 times and wanted to find the probability of it turning up "heads" exactly 10 times, the function looks like this:

=BINOMDIST(10,20,0.5,FALSE)

The function returns the value 0.176197052. If you wanted to find the probability of getting
10 or fewer heads, you replace the FALSE with TRUE, and the function returns the value 0.588098526.

Using Excel's CRITBINOM Function

The acceptance criterion function, CRITBINOM, is used for quality control of a production process. You use this function to find the maximum number of defective items that a person can find in a lot and still allow acceptance of the lot. Inspectors should accept the lot if they find this number or fewer defective items and reject the lot if they find more defective items.

To determine the acceptance criterion, you need to know the number of items in the lot, the probability of accepting each item, and the producer's allowable risk (alpha) for rejecting an acceptable lot.

The CRITBINOM function uses the following syntax:

=CRITBINOM (trials, probability_s, alpha)

where trials is the number of trials, probability's is the probability of a success on each trial,
and alpha is the criterion value. Probability's and alpha are both between 0 and 1.

Using Excel's NEGBINOMDIST Function

If the number of successes is fixed in a binomial distribution and you want to find the number of trials, use the NEGBINOMDIST function. This function returns the probability that there will be a certain number of failures before the threshold number of successes, given the constant probability of a success.

For example, if you need to find 20 straight 2 by 4s from a stack, and you know the probability that a board in the stack is straight is 0.2 (20%), you can use the NEGBINOMDIST to find that there is about a 2% probability that you will reject 75 boards before finding all 20 straight ones.

The NEGBINOMDIST function uses the following syntax:

=NEGBINOMDIST (number failures, number successes, probability of success)

For this example, the function looks like this:

=negbinomdist (75, 20, 0.2)

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Tuesday, March 23, 2010

Scientific probability distributions with Microsoft Excel


Image : http://www.flickr.com


A binomial distribution describes the result of a multi-step experiment, consisting
n identical trials, where each attempt ends either in success or failure and the probability of
p is a success does not change from experiment to experiment. This is a useful statistical analysis can be done relatively easily using Microsoft Excel using the Excel BINOMDIST, CRITBINOM and NEGBINOMDIST functions.

Note, however, that for the manufacture of binomial probability theory, the test should alsobe independent, so the success of a procedure does not affect the probability of success in another trial. Binomial random variable x is the number of successes observed in animal studies No

When samples are not replaced and thus the result of a process to change the probability of success in another job, you must use the hypergeometric probability distribution function in Excel.

BINOMDIST using the Excel function

For example, if you're an n times and "heads"as a success, then the random variable
x is the number of animals observed in n tosses. You can take the values 1,2,3 ,..., n with different probabilities.

BINOMDIST uses the following syntax:

BINOMDIST = (x, n, p, cumulative)

If you find the probability of exactly x successes, enter false data, as the fourth () returns a cumulative basis. If you find the probability of x or less success, to give TRUE as the fourth argument.

For example, if yousaw a coin 20 times and wanted the chance that I get "heads" exactly 10 times Flip found, the function is similar to the following:

= BINOMDIST (10,20,0.5, FALSE)

The function returns the value 0.176197052. If you find that the probability
10 or less heads, you replace the FALSE with TRUE, and the function returns the value 0.588098526.

Using the Excel function CRITBINOM

The adoption of the objective function, CRITBINOM is used for quality controlproduction process. Use this function to the maximum number of defective products, which are to find a person in a game and still allow for the acceptance of the lot. Inspectors should accept the lot if you can find this number or fewer defective parts and reject the lot if you want to find items you worse.

To determine the criterion of acceptability is necessary to know the number of elements in the crowd, the probability of accepting each item, and acceptable risk of producers' (alpha) for rejecting anacceptable amount.

CRITBINOM function uses the following syntax:

= CRITBINOM (studies probability_s, alpha)

experiments in which the number of attempts, the probability is the probability of success for each subject,
and alpha-value is the criterion. Probability and alpha are both between 0 and 1

NEGBINOMDIST using the Excel function

If the number of successes in a binomial distribution company and want to find the number of attempts to use the NEGBINOMDISTFunction. This function returns the probability that a certain number of failures before the number of critical success as the probability of success constant.

For example, if you) are up 20 2 directly by 4s from a stack, and you know the probability that a card in the stack is only 0.2 (is 20%, you can use to determine that NEGBINOMDIST is a 2% probability that you reject 75 boards before the search, even after all 20

TheNEGBINOMDIST function uses the following syntax:

NEGBINOMDIST = (number of errors, the number of successes, the probability of success)

In this example, the function is similar to the following:

NEGBINOMDIST = (75, 20, 0.2)

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Monday, March 22, 2010

Binomial Probability Distributions with Microsoft Excel


Image : http://www.flickr.com


A binomial distribution describes the outcome of a multi-step experiment, consisting of
n identical trials, where each trial ends in either a success or a failure and the probability of
a success p does not change from trial to trial. This useful statistical analysis can be performed relatively easily using Microsoft Excel using the Excel BINOMDIST, CRITBINOM and NEGBINOMDIST functions.

Note, however, that when making binomial probability calculations, the trials must also be independent so that success in one trial does not affect the probability of success in another trial. The binomial random variable x is the number of successes observed in n trials.

If samples are not replaced, and therefore the outcome of one trial changes the probability of success in another trial, you need to use the hypergeometric probability distribution Excel function.

Using Excel's BINOMDIST Function

For example, if you flip a coin n times and "heads" is called a success, then the random variable
x would be the number of heads observed in n flips. It could take the values 1,2,3,...,n with different probabilities.

The BINOMDIST function uses the following syntax:

=BINOMDIST(x,n,p,cumulative)

If you want to find the probability of exactly x successes, enter FALSE as the fourth (cumulative) argument. If you want to find the probability of x or fewer successes, enter TRUE as the fourth argument.

For example, if you were to flip a fair coin 20 times and wanted to find the probability of it turning up "heads" exactly 10 times, the function looks like this:

=BINOMDIST(10,20,0.5,FALSE)

The function returns the value 0.176197052. If you wanted to find the probability of getting
10 or fewer heads, you replace the FALSE with TRUE, and the function returns the value 0.588098526.

Using Excel's CRITBINOM Function

The acceptance criterion function, CRITBINOM, is used for quality control of a production process. You use this function to find the maximum number of defective items that a person can find in a lot and still allow acceptance of the lot. Inspectors should accept the lot if they find this number or fewer defective items and reject the lot if they find more defective items.

To determine the acceptance criterion, you need to know the number of items in the lot, the probability of accepting each item, and the producer's allowable risk (alpha) for rejecting an acceptable lot.

The CRITBINOM function uses the following syntax:

=CRITBINOM (trials, probability_s, alpha)

where trials is the number of trials, probability's is the probability of a success on each trial,
and alpha is the criterion value. Probability's and alpha are both between 0 and 1.

Using Excel's NEGBINOMDIST Function

If the number of successes is fixed in a binomial distribution and you want to find the number of trials, use the NEGBINOMDIST function. This function returns the probability that there will be a certain number of failures before the threshold number of successes, given the constant probability of a success.

For example, if you need to find 20 straight 2 by 4s from a stack, and you know the probability that a board in the stack is straight is 0.2 (20%), you can use the NEGBINOMDIST to find that there is about a 2% probability that you will reject 75 boards before finding all 20 straight ones.

The NEGBINOMDIST function uses the following syntax:

=NEGBINOMDIST (number failures, number successes, probability of success)

For this example, the function looks like this:

=negbinomdist (75, 20, 0.2)

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