Difference between revisions of "Manuals/calci/HYPGEOMDIST"

Revision as of 02:41, 10 December 2013

HYPGEOMDIST(n1,n2,n3,n4)

$n1$ is the sample's success.
$n2$ is the sample's size.
$n3$ is population's success.
$n4$ is the population size.

Description

This function gives the result of Hypergeometric distribution.
This distribution is a discrete probability distribution which is contrast to the binomial distribution.
A hypergeometric random variable is the number of successes that result from a hypergeometric experiment.
The probability distribution of a hypergeometric random variable is called a hypergeometric distribution.
In HYPGEOMDIST(n1,n2,n3,n4) where n1 is thenumber of items in the Sample that are classified as successes.
n2 is the total number of items in the sample.
n3 is thenumber of items in the population that are classified as successes and n4 is the total number of items in the sample.
The following conditions are applied to the Hypergeometric distribution:

This distribution is applies to sampling without replacement from a finite population whose elements can be classified into two categories like success or Failure.
The population or set to be sampled consists of N individuals, objects,or elements
Each individual can be success (S) or a failure (F),

and there areM successes in the population.

A sample of n individuals is selected without replacement in such a way that each subset of size n is equally likely to be chosen. The Hyper geometric probability distribution is:

P(X=x)=h(x;n,M,N)=(M (N-M

                                    x)           n-x)         /(N     
                                                                      n)  for x is an integer satisfying   max(0, n-N+M)<=x<=min(n,M). where x is sample's success.

n is the sample's size.
M is population's success and N is the population size.
Here we can give any positive real numbers.
Suppose we are assigning any decimals numbers it will change in to Integers.
This function will give result as error when

Any one of the argument is nonnumeric.
n1<0 or n1 is greater than the smaller value of n2 or n3.
n1 is less than the bigger of 0 or(n2-n4+n3)
n2<=0 or n2>n4
n3<=0 or n3>n4 or n4<=0"

Examples

HARMEAN(1,2,3,4,5)=2.18978102189781
HARMEAN(20,25,32,41)=27.4649361523969
HARMEAN(0.25,5.4,3.7,10.1,15.2)=1.0821913906985883
HARMEAN(3,5,0,2)=NAN
HARMEAN(1,-2,4)=NAN

References

Correlation

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-<div style="font-size:30px">'''<div style="font-size:30px">'''HYPGEOMDIST(n1,n2,n3,n4)'''</div><br/>
+<div style="font-size:30px">'''HYPGEOMDIST(n1,n2,n3,n4)'''</div><br/>
 *<math>n1</math> is the sample's success.
 *<math>n2</math> is the sample's size.
-*<math>n3</math> is population's success
+*<math>n3</math> is population's success.
 *<math>n4</math> is the population size.
 ==Description==
-"This function gives the result of Hypergeometric distribution.
+*This function gives the result of Hypergeometric distribution.
-This distribution  is a discrete probability distribution which is contrast to the binomial distribution.
+*This distribution  is a discrete probability distribution which is contrast to the binomial distribution.
-A hypergeometric random variable is the number of successes that result from a hypergeometric experiment.
+*A hypergeometric random variable is the number of successes that result from a hypergeometric experiment.
-The probability distribution of a hypergeometric random variable is called a hypergeometric distribution.
+*The probability distribution of a hypergeometric random variable is called a hypergeometric distribution.
-In  HYPGEOMDIST(n1,n2,n3,n4) where n1 is thenumber of items in the Sample  that are classified as successes.
+*In  HYPGEOMDIST(n1,n2,n3,n4) where n1 is thenumber of items in the Sample  that are classified as successes.
-n2 is the total number of items in the sample.
+*n2 is the total number of items in the sample.
-n3 is thenumber of items in the population  that are classified as successes and n4 is the total number of items in the sample.
+*n3 is thenumber of items in the population  that are classified as successes and n4 is the total number of items in the sample.
-The following conditions are applied to the Hypergeometric distribution:
+*The following conditions are applied to the Hypergeometric distribution:
-.This distribution is applies to sampling without replacement from a finite population whose elements can be classified into two  categories like success or Failure.
+#This distribution is applies to sampling without replacement from a finite population whose elements can be classified into two  categories like success or Failure.
-.The population or set to be sampled consists of N individuals, objects,or elements
+#The population or set to be sampled consists of N individuals, objects,or elements
-.Each individual can be  success (S) or a failure (F),
+#Each individual can be  success (S) or a failure (F),
 and there areM successes in the population.
-. A sample of n individuals is selected without replacement in such a way that each subset of size n is equally likely to be chosen. The Hyper geometric probability distribution is:
+#A sample of n individuals is selected without replacement in such a way that each subset of size n is equally likely to be chosen. The Hyper geometric probability distribution is:
 P(X=x)=h(x;n,M,N)=(M          (N-M
                                       x)           n-x)         /(N
-                                                                        n)  for x is an integer satisfying   max(0, n-N+M)<=x<=min(n,M). where x is sample's success.n is the sample's size.M is population's success and N is the population size. Here we can give any positive real numbers. Suppose we are assigning any decimals numbers it will change in to Integers. This function will give result as error when 1. Any one of the argument is nonnumeric.
+                                                                        n)  for x is an integer satisfying   max(0, n-N+M)<=x<=min(n,M). where x is sample's success.
-.n1<0 or n1 is greater than the smaller value of n2 or n3.
+*n is the sample's size.
-.n1 is less than the bigger of 0 or(n2-n4+n3)
+*M is population's success and N is the population size.
-. n2<=0 or n2>n4
+*Here we can give any positive real numbers.
-.n3<=0 or  n3>n4 or n4<=0"
+*Suppose we are assigning any decimals numbers it will change in to Integers.
+*This function will give result as error when
-==Examples==
+#Any one of the argument is nonnumeric.
+#n1<0 or n1 is greater than the smaller value of n2 or n3.
-Draw 6 cards from a deck without replacement.
+#n1 is less than the bigger of 0 or(n2-n4+n3)
-What is the probability of getting two hearts?
+#n2<=0 or n2>n4
-Here M = 13 number of hearts
+#n3<=0 or  n3>n4 or n4<=0"
-N = 52 total number of cards
-so N-M= 52-13= 39 and
-x=2,n=6 so n-x=6-2=4
-HYPGEOMDIST(2,6,13,52)=0.315129882
-.42 balls are numbered 1 - 42.
-You select six numbers between 1 and 42. What is the probability that they contain
-(i)match 3?
-(ii) match 4?
-(i)Here M= 6,N=42,x=3and n=6
-HYPGEOMDIST(3,6,6,42)=0.02722185
-(ii)Here M= 6,N=42,x=4and n=6
-HYPGEOMDIST(4,6,6,42)=0.001801446
-.
-==See Also==
-*[[Manuals/calci/BINOMDIST  | BINOMDIST ]]
-*[[Manuals/calci/COMBIN  | COMBIN ]]
-*[[Manuals/calci/FACT  | FACT ]]
-==References==
-[http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient| Correlation]
-(ar1,ar2)'''</div><br/>
-*<math>ar1</math> and <math>ar2 </math> are the set of values.
-==Description==
-*This function gives the correlation coefficient of the 1st set(<math>ar1</math>) of values and 2nd set(<math>ar2</math>) of values.
-*Correlation is a statistical technique which shows the relation of strongly paired variables.
-*For example, test average and study time are related; those who spending more time to study will get high marks and Average will go down for those who spend less time for studies.
-*There are  different correlation techniques to measure the Degree of Correlation.
-*The most common of these is the Pearson Correlation Coefficient  denoted by <math>r_xy</math>.
-*The main result of a correlation is called the Correlation Coefficient(<math>r</math>)which  ranges from -1 to +1.
-*The <math>r</math> value is positive i.e +1  when the two set values increase together then it is the perfect Positive Correlation.
-*The <math>r</math> value is negative i.e. (-1)  when one value decreases as the other increases then it is called Negative Correlation.
-*Suppose the <math>r</math> value is 0 then there is no correlation (the values don't seem linked at all).
-*If we have a series of <math>n</math> measurements of <math>X</math> and <math>Y</math> written as <math>xi</math> and <math>yi</math> where <math>i = 1, 2,...n</math> then the Sample Correlation Coefficient is:
- <math>CORREL(X,Y)= r_{xy}= \frac{\sum_{i=1}^n (xi-\bar x)(yi-\bar y)}{\sqrt{ \sum_{i=1}^n (xi-\bar x)^2 \sum{i=1}^n (yi-\bar y)^2}}</math>
-*<math>\bar x</math> and <math>\bar y</math> are the sample means of <math>X</math> and <math>Y</math>.
-*This function will give the result as error when
-.<math>ar1</math> and <math>ar2</math> are non-numeric or different number of data points.
-.<math>ar1</math> or <math>ar2</math> is empty
-.The denominator value is zero.
-*Suppose <math>ar1</math> and <math>ar2</math> contains any text, logical values, or empty cells, like that values are ignored.
 ==Examples==
-#Find the correlation coefficients for X and Y values are given below :X={1,2,3,4,5};  Y={11,22,34,43,56}
+#HARMEAN(1,2,3,4,5)=2.18978102189781
-=CORREL(A4:A8,B4:B8)=0.99890610723867
+#HARMEAN(20,25,32,41)=27.4649361523969
-#The following table gives the math scores and times taken to run 100 m for 10 friends:SCORE(X)={52,25,35,90,76,40}; TIME TAKEN(Y)={11.3,12.9,11.9,10.2,11.1,12.5}
+#HARMEAN(0.25,5.4,3.7,10.1,15.2)=1.0821913906985883
-=CORREL(A5:A10,B5:B10)= -0.93626409417769
+#HARMEAN(3,5,0,2)=NAN
-#Find the correlation coefficients for X and Y values are given below :X={-4,11,34,87};Y={9,2,59,24}
+#HARMEAN(1,-2,4)=NAN
-=CORREL(A1:A4,B1:B4)=0.353184665607273
 ==See Also==
-*[[Manuals/calci/COVAR  | COVAR ]]
+*[[Manuals/calci/AVERAGE  | AVERAGE ]]
-*[[Manuals/calci/FISHER  | FISHER ]]
+*[[Manuals/calci/GEOMEAN  | GEOMEAN ]]
 ==References==
 [http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient| Correlation]

Difference between revisions of "Manuals/calci/HYPGEOMDIST"

Revision as of 02:41, 10 December 2013

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References

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