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Package ‘moments’
May 2, 2022
Type Package
Title Moments, Cumulants, Skewness, Kurtosis and Related Tests
Version 0.14.
Date 2015-01-
Author Lukasz Komsta lukasz.komsta@umlub.pl, Frederick Novomestky
fnovomes@poly.edu
Maintainer Lukasz Komsta lukasz.komsta@umlub.pl
Description Functions to calculate: moments, Pearson's kurtosis, Geary's kurtosis and skewness; tests related to them (Anscombe-Glynn, D'Agostino, Bonett-Seier).
License GPL (>= 2)
URL https://www.r-project.org, http://www.komsta.net/
NeedsCompilation no
Repository CRAN
Date/Publication 2022-05-02 13:01:55 UTC
R topics documented:
agostino.test......................................... 2 all.cumulants........................................ 3 all.moments......................................... 4 anscombe.test........................................ 5 bonett.test.......................................... 6 central2raw......................................... 8 geary............................................ 9 jarque.test.......................................... 10 kurtosis........................................... 11 moment........................................... 11 raw2central......................................... 12 skewness.......................................... 13
Index 15
2 agostino.test
agostino.test D’Agostino test of skewness
Description
Performs D’Agostino test for skewness in normally distributed data.
Usage
agostino.test(x, alternative = c("two.sided", "less", "greater"))
Arguments
x a numeric vector of data values. alternative a character string specifying the alternative hypothesis, must be one of ’"two.sided"’ (default), ’"greater"’ or ’"less"’. You can specify just the initial letter.
Details
Under the hypothesis of normality, data should be symmetrical (i.e. skewness should be equal to zero). This test has such null hypothesis and is useful to detect a significant skewness in normally distributed data.
Value
A list with class htest containing the following components:
statistic the list containing skewness estimator and its transformation. p.value the p-value for the test. alternative a character string describing the alternative hypothesis. method a character string indicating what type of test was performed. data.name name of the data argument.
Author(s)
Lukasz Komsta
References
D’Agostino, R.B. (1970). Transformation to Normality of the Null Distribution of G1. Biometrika, 57, 3, 679-681.
See Also
skewness
4 all.moments
Examples
set.seed(1234) x <- rnorm(10000) mu.raw.x <- all.moments( x, order.max=6 ) all.cumulants( mu.raw.x ) M <- matrix( x, nrow=1000, ncol=10 ) mu.raw.M <- all.moments( M, order.max=6 ) all.cumulants( mu.raw.M ) D <- data.frame( M ) mu.raw.D <- all.moments( D, order.max=6 ) all.cumulants( mu.raw.D )
all.moments Statistical Moments
Description
This function computes all the sample moments of the chosen type up to a given order.
Usage
all.moments(x, order.max = 2, central = FALSE, absolute = FALSE, na.rm = FALSE)
Arguments
x A numeric vector, matrix or data frame of data. For matrices and data frames, each column is a random variable order.max the maximum order of the moments to be computed with a default value of 2. central a logical value, if TRUE, central moments are computed. Otherwise, raw mo- ments are computed absolute a logical value, if TRUE, absolute moments are computed. Otherwise, standard moments are computed na.rm a logical value, if TRUE, remove NA values. Otherwise, keep NA values
Details
The minimum value for order.max is 2. The function stops running for values less than 2 and the message "maximum order whould be at least 2" is displayed on standard output.
Value
A vector, matrix or data frame of moments depending on the nature of the argument x. If x is a vector, then the value returned is a vector, say mu, where mu[1] is the order 0 moment, mu[2] is the order 1 moment and so forth. If x is a matrix or data frame, then the value returned is a matrix or data frame, respectively. In this case, suppose mu is the value returned. Then, row vector mu[1,] contains the order 0 moments, mu[2,] contains the order 1 moments and so forth.
anscombe.test 5
Author(s)
Frederick Novomestky fnovomes@poly.edu
References
Papoulis, A., Pillai, S. U. (2002) Probability, Random Variables and Stochastic Processes, Fourth Edition, McGraw-Hill, New York, 146-147.
See Also
moment, raw2central
Examples
set.seed(1234) x <- rnorm(10000) all.moments( x, order.max=4 ) all.moments( x, central=TRUE, order.max=4 ) all.moments( x, absolute=TRUE, order.max=4 ) all.moments( x, central=TRUE, absolute=TRUE, order.max=4 ) M <- matrix( x, nrow=1000, ncol=10 ) all.moments( M, order.max=4 ) all.moments( M, central=TRUE, order.max=4 ) all.moments( M, absolute=TRUE, order.max=4 ) all.moments( M, central=TRUE, absolute=TRUE, order.max=4 ) D <- data.frame( M ) all.moments( D, order.max=4 ) all.moments( D, central=TRUE, order.max=4 ) all.moments( D, absolute=TRUE, order.max=4 ) all.moments( D, central=TRUE, absolute=TRUE, order.max=4 )
anscombe.test Anscombe-Glynn test of kurtosis
Description
Performs Anscombe-Glynn test of kurtosis for normal samples
Usage
anscombe.test(x, alternative = c("two.sided", "less", "greater"))
Arguments
x a numeric vector of data values. alternative a character string specifying the alternative hypothesis, must be one of ’"two.sided"’ (default), ’"greater"’ or ’"less"’. You can specify just the initial letter.
bonett.test 7
Arguments
x a numeric vector of data values. alternative a character string specifying the alternative hypothesis, must be one of ’"two.sided"’ (default), ’"greater"’ or ’"less"’. You can specify just the initial letter.
Details
Under the hypothesis of normality, data should have Geary’s kurtosis equal to sqrt(2/pi) (0.7979). This test has such null hypothesis and is useful to detect a significant difference of Geary’s kurtosis in normally distributed data.
Value
A list with class htest containing the following components:
statistic the list containing Geary’s kurtosis estimator and its transformation. p.value the p-value for the test.
alternative a character string describing the alternative hypothesis. method a character string indicating what type of test was performed. data.name name of the data argument.
Author(s)
Lukasz Komsta
References
Bonett, D.G., Seier, E. (2002) A test of normality with high uniform power. Computational Statis- tics and Data Analysis, 40, 435-445.
See Also
geary
Examples
set.seed(1234) x = rnorm(1000) geary(x) bonett.test(x)
8 central2raw
central2raw Central to raw moments
Description
This function transforms a vector, matrix or data frame of central moments to a vector, matrix or data frame of raw moments.
Usage
central2raw(mu.central,eta)
Arguments
mu.central A numeric vector, matrix or data frame of central moments. For a vector, mu.central[0] is the order 0 central moment, mu.central[1] is the order 1 cen- tral moment and so forth. For a matrix or data frame, row vector mu.central[0,] contains the order 0 central moments, row vector mu.central[1,] contains the order 1 central moments and so forth. eta A numeric vector of sample mean or expected values
Value
A vector matrix or data frame of raw moments. For matrices and data frame, column vectors correspond to different random variables.
Author(s)
Frederick Novomestky fnovomes@poly.edu
References
Papoulis, A., Pillai, S. U. (2002) Probability, Random Variables and Stochastic Processes, Fourth Edition, McGraw-Hill, New York, 146-147.
See Also
moment, all.moments, raw2central
Examples
set.seed(1234) x <- rnorm(10000) mu.raw.x <- all.moments( x, order.max=4 ) eta.x <- mu.raw.x[2] mu.central.x <- all.moments( x, central=TRUE, order.max=4 ) central2raw( mu.central.x, eta.x ) mu.raw.x
10 jarque.test
Examples
set.seed(1234) geary(rnorm(1000))
jarque.test Jarque-Bera test for normality
Description
This function performs the Jarque-Bera test on the given data sample to determine if the data are sample drawn from a normal population.
Usage
jarque.test(x)
Arguments
x a numeric vector of data
Details
Under the hypothesis of normality, data should be symmetrical (i.e. skewness should be equal to zero) and have skewness chose to three. The Jarque-Bera statistic is chi-square distributed with two degrees of freedom.
Value
A list with class htest containing the following components:
statistic the list containing the Jarque-Bera statistic p.value the p-value for the test. alternative a character string describing the alternative hypothesis. method a character string indicating what type of test was performed. data.name name of the data argument.
Author(s)
Frederick Novomestky fnovomes@poly.edu
References
Jarque, C. M., Bera, A. K. (1980) Efficient test for normality, homoscedasticity and serial indepen- dence of residuals, Economic Letters, Vol. 6 Issue 3, 255-259.
kurtosis 11
Examples
set.seed( 1234 ) x <- rnorm( 1000 ) jarque.test( x )
kurtosis Pearson’s measure of kurtosis
Description
This function computes the estimator of Pearson’s measure of kurtosis.
Usage
kurtosis(x, na.rm = FALSE)
Arguments
x a numeric vector, matrix or data frame. na.rm logical. Should missing values be removed?
Author(s)
Lukasz Komsta
See Also
geary, anscombe.test
Examples
set.seed(1234) kurtosis(rnorm(1000))
moment Statistical Moments
Description
This function computes the sample moment of specified order.
Usage
moment(x, order = 1, central = FALSE, absolute = FALSE, na.rm = FALSE)
skewness 13
References
Papoulis, A., Pillai, S. U. (2002) Probability, Random Variables and Stochastic Processes, Fourth Edition, McGraw-Hill, New York, 146-147.
See Also
moment, all.moments, central2raw
Examples
set.seed(1234) x <- rnorm(10000) mu.raw.x <- all.moments( x, order.max=4 ) mu.central.x <- all.moments( x, central=TRUE, order.max=4 ) raw2central( mu.raw.x ) mu.central.x M <- matrix( x, nrow=1000, ncol=10 ) mu.raw.M <- all.moments( M, order.max=4 ) mu.central.M <- all.moments( M, central=TRUE, order.max=4 ) raw2central( mu.raw.M ) mu.central.M D <- data.frame( M ) mu.raw.D <- all.moments( D, order.max=4 ) mu.central.D <- all.moments( D, central=TRUE, order.max=4 ) raw2central( mu.raw.D ) mu.central.D
skewness Skewness of the sample
Description
This function computes skewness of given data.
Usage
skewness(x, na.rm = FALSE)
Arguments
x a numeric vector, matrix or data frame. na.rm logical. Should missing values be removed?
Author(s)
Lukasz Komsta
14 skewness
See Also
agostino.test
Examples
set.seed(1234) skewness(rnorm(1000))
