```Statistical calculation forms

[Descriptive statistics]
1.  Statistical calculation form for descriptive statistics 1.  http://www.wwq.jp/javascript/p520e.html
Statistics by "one variable" are calculated. Distribution is arbitrary.
Total frequency, Maximum value, Minimum value, Total(weighted), Mean, Total of square, Mean of square,
Total variation, Variance, Relative variance, Standard deviation, Coefficient of variation, Mean deviation,
Relative mean deviation, Mean of third power, Third moment(around mean), Skewness, Absolute third moment,
Third kurtosis, Mean of fourth power, Fourth moment(around mean), Kurtosis(ratio of moments),
Kurtosis(minus 3), Geometric mean, Harmonic mean.

2.  Statistical calculation form for descriptive statistics 2.  http://www.wwq.jp/javascript/p520e2.html
Statistics by "two variables" are calculated. Distributions are arbitrary.
Total frequency, Maximum of x, Minimum of x, Maximum of y, Minimum of y, Total of x(weighted), Total of
y(weighted), Mean of x, Mean of y, Total variation of x, Total variation of y, Variance of x, Variance
of y, Standard deviation of x, Standard deviation of y, Coefficient of variation of x, Coefficient of
variation of y, Total covariation of x and y, Covariance of x and y, Correlation coefficient of x and y,
For a regression line y=a+bx, a, b, Coefficient of determination.

3.  Statistical calculation form for descriptive statistics 3.  http://www.wwq.jp/javascript/p520e3.html
Statistics by "three variables" are calculated. Distributions are arbitrary.
Total frequency, Maximum of each variable, Minimum of each variable, Total of each variable(weighted),
Mean of each variable, Total variation of each variable, Variance of each variable, Standard deviation
of each variable, Coefficient of variation of each variable, Total covariations between variables,
Covariances between variables, Value of covariance determinant(order of zxy) and its cofactors, Simple
Å@correlation coefficients between variables, Partial correlation coefficients between variables, For the
least squares regression plane z=a+bx+cy; a,b,c, Residual sum of z, Residual variance of z, Coefficient
of determination of z for x and y, Multiple correlation coefficient of z for x and y.

4.  Calculation form of intraclass correlation coefficient  http://www.wwq.jp/javascript/intracorre.html
Number of data is up to 50. Number of variables is up to 9. Distributions are arbitrary.
Total frequency, Total mean, Within variance, Between variance, Total variance, Intraclass correlation
coefficient.

Å@
[Inductive statistics]
1.  Calculation form of estimates 1.  http://www.wwq.jp/javascript/p520se.html
Random variables are to be sample drawn independently with equal probability from an arbitrary population.
Point estimations are available for any populations. Interval estimation necesitates the related probability
distribution.
Total frequency, Total of x(weighted), Mean(unbiased), Variance(unbiased), Standard deviation, Coefficient
of variation, Variance of sample mean(unbiased), Standard error of sample mean, Variance of variance(un-
biased), Standard error of sample variance, Third moment(around mean, unbiased), Skewness, Fourth moment
(around mean, unbiased), Kurtosis(ratio of moments), Kurtosis(minus 3), Kutopsis(minus 3, Excel).Å@

2.  Calculation form of estimates 2.  http://www.wwq.jp/javascript/p520fe.html
Random variables are to be sample drawn with uqual probability without replacement from an arbitrary finite
population. Point estimations are available for any populations. Interval estimation necesitates the related
probability distribution.
Total frequency, Total of x(weighted), Mean(unbiased), Variance(unbiased), Standard deviation, Coefficient
of variation, Variance of sample mean(unbiased), Standard error of sample mean, Variance of variance(un-
biased), Standard error of sample variance, Third moment(around mean, unbiased), Skewness, Fourth moment
(around mean, unbiased), Kurtosis(ratio of moments), Kurtosis(minus 3).Å@

3.  Calculation form of estimates 3.  http://www.wwq.jp/javascript/p520se2.html
Two-dimensional random variables are to be sample drawn independently with equal probability from an
arbitrary two-dimensional population. Point estimations are available for any  populations. Interval
estimation necesitates the related probability distribution.
Total frequency, Total of x(weighted), Total of y(weighted), Mean of x(unbiased), Mean of y(unbiased),
Variance of x(unbiased), Variance of y(unbiased), Standard deviation of x, Standard deviation of y,
Coefficient of variation of x, Coefficient of variation of y, Covariance of x and y(unbiased),
Correlation coefficient of x and y, For a regression line y=a+bx, a, b, Coefficient of determination of y.

4.  Calculation form of estimates 4.  http://www.wwq.jp/javascript/p520se2b.html
In variables (xi,yi)(i=1,2,3,...,n), x is a variable that takes n known values xi and y is a random variable
that takes n values yi drawn independently from n populations. Here E(yi)=a+bxi, and V(yi)=É–2, where a, b
and É–2 are common through all populations. a, b, É–2, etc. are estimated by sample (xi,yi). Point estimations
are available for any populations. Interval estimation necesitates the related probability distribution.
Sample size, Mean of x, Mean of y, Total variation of x, Total variation of y, Total covariation of x and y,
Correlation coefficient of x and y, Coefficient of determination of y, For a regression line y=a+bx,
Éø(unbiased for a), É¿(unbiased for b), Sample residual sum of squares, Variance unbiased for common É–2,
Estimator for common standard deviation É–, Sample variance of Éø(unbiased for V(Éø)), Sample standard
deviation of Éø, Sample variance of É¿(unbiased for V(É¿)), Sample standard deviation of É¿, Sample
covariance of Éø and É¿(unbiased for Cov(Éø,É¿)), Sample correlation coefficient of Éø and É¿, For time
series, Durbin-Watson statistic.

5.  Calculation form of estimates 5  http://www.wwq.jp/javascript/p520se3.html
Three-dimensional random variables are to be sample drawn independently with equal probability from an
arbitrary three-dimensional population. Point estimations are available for any  populations. Interval
estimation necesitates the related probability distribution.
Total frequency, Total of each variable(weighted), Mean of each variable(unbiased), Total variation of
each variable, Unbiased variance of each variable, Variance of each variable, Standard deviation of
each variable, Coefficient of variation of each variable, Total covariations between variables,
Covariances between variables(unbiased), Value of covariance determinant(order of zxy) and its cofactors,
Simple correlation coefficients between variables, Partial correlation coefficients between variables,
For the least squares regression plane z=a+bx+cy; a,b,c, Residual sum of z, Residual variance of z,
Coefficient of determination of z for x and y, Multiple correlation coefficient of z and (x,y).

6.  Calculation form of estimates 6.  http://www.wwq.jp/javascript/p520se3b.html
In variables (xi,yi,zi)(i=1,2,3,...,n), x and y are variables which take n known values xi and yi, respec-
tively. z is a random variable that takes n values zi drawn independently from n populations. Here E(zi)
=a+bxi+cyi, and V(zi)=É–2, where a, b, c and É–2 are common through all populations. a, b, c, É–2, etc. are
estimated by sample (xi,yi,zi). Point estimations are available for any populations. Interval estimation
necesitates the related probability distribution.
Sample size, Mean of each variable, Total variation of each variable, Total covariations between
variables, Covariances between variables, Simple correlation coefficients of variables, Value of
covariance determinant(order of zxy) and its cofactors, Partial correlation coefficients of variables, For
the least squares regression plane z=a+bx+cy; Éø(unbiased for a), É¿(unbiased for b), É¡(unbiased for c),
Sum of residual squares of z, Residual variance of z, Variance unbiased for common É–2 and its standard
deviation, Sample variances of Éø,É¿,É¡ unbiased for their proper variances and their standard deviations,
Sample covariances of the two of Éø,É¿,É¡(unbiased for their proper covariances), Sample correlation
coefficients of the two of Éø,É¿,É¡, Coefficient of determination of z by x and y, Multiple correlation
coefficient of z and x,y,  For time series, Durbin-Watson statistic.

[Statistical distributions]
1.  Calculation form 1 for normal distribution http://www.wwq.jp/javascript2/normale1.html
Probabilities for given interval are obtained.

2.  Calculation form 2 for normal distribution http://www.wwq.jp/javascript2/normale2.html
Related value for given area(probability) is obtained.

3.  Calculation form 1 for t distribution http://www.wwq.jp/javascript2/te1.html
Probabilities for given interval are obtained.

4.  Calculation form 2 for t distribution http://www.wwq.jp/javascript2/te2.html
Related value for given area(probability) is obtained.

5.  Calculation form 1 for É‘2 distribution http://www.wwq.jp/javascript2/kai2e1.html
Probabilities for given interval are obtained.

6.  Calculation form 2 for É‘2 distribution http://www.wwq.jp/javascript2/kai2e2.html
Related value for given area(probability) is obtained.

Calculation of fundamental functions

1.  Calculation of fundamental functions.  http://www.wwq.jp/javascript/mathcale.html
Fundamental functions, exponential, logarithmic, trigonometric, hyperbolic,
gamma and beta function.

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