Package ‘staTools’
March 17, 2015
Title Statistical Tools for Social Network Analysis
Version 0.1.0
Author Alessandro Bessi
Maintainer Alessandro Bessi <[email protected]>
Description A collection of statistical tools for social network analysis, with strong emphasis on the analysis of discrete powerlaw distributions and statistical hypothesis tests.
Depends R (>= 3.1.1)
License GPL (>= 2)
LazyData true
LinkingTo Rcpp
Imports Rcpp, VGAM, magicaxis
NeedsCompilation yes
Repository CRAN
Date/Publication 2015-03-17 21:00:02
R topics documented:
cdf . . . .
data_cdf .
ddispl . .
displo . .
fastsum .
getXmin .
getXmin2
inspect . .
len . . . .
MAE . .
MAPE . .
moby . .
MPE . . .
MSE . . .
pdispl . .
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2
2
3
3
4
4
5
6
6
7
7
8
8
9
9
2
data_cdf
plotfit . . .
plothill . . .
plotmultifit
plotols . . .
pmf . . . .
rdispl . . .
RMSE . . .
std . . . . .
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Index
cdf
Cumulative Distribution Function
Empirical Cumulative Distribution Function.
Usage
cdf(x)
Arguments
A vector of observations.
Examples
x = rdispl(n = 1e4, xmin = 10, alpha = 2.5, xmax = 1e5)
obs = cdf(x)$x
ecdf = cdf(x)$y
data_cdf
Data Cumulative Distribution Function
Description
Empirical Cumulative Distribution Function of Data.
Usage
data_cdf(x)
Arguments
x
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10
10
11
11
12
12
13
13
14
Description
x
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.
A vector of observations.
ddispl
3
Examples
x = rdispl(n = 1e4, xmin = 10, alpha = 2.5, xmax = 1e5)
ecdf = data_cdf(x)
ddispl
Discrete Powerlaw Probability Mass Function
Description
Probability mass function for the discrete power law distribution with parameters xmin and alpha.
Usage
ddispl(x, xmin, alpha, log = FALSE)
Arguments
x
Vector of quantiles.
xmin
The lower bound of the powerlaw distribution.
alpha
The scaling parameter.
log
Logical, whether return log values. By default is set to FALSE.
Examples
x = rdispl(n = 1e4, xmin = 10, alpha = 2.5)
ddispl(x, xmin = 10, alpha = 2.5, log = FALSE)
displo
Discrete Powerlaw Object
Description
This function allows to create a discrete powerlaw object to analyze.
Usage
displo(x, summary = TRUE)
Arguments
x
A vector containing the observations.
summary
Logical, whether print a summary with some information concerning data. By
default is set to TRUE.
4
getXmin
Examples
data(moby)
x = moby
o = displo(x)
fastsum
Fast Sum implemented in Cpp.
Description
Cpp function which speed up the computation of the Hurwitz zeta function.
Usage
fastsum(i, xmin, alpha)
Arguments
i
An integer.
xmin
An integer.
alpha
A real number greater than 1.
getXmin
Lower bound estimator for discrete powerlaw distributions
Description
Lower bound estimator for discrete powerlaw distributions.
Usage
getXmin(o, g = 1, c = 90, k = 5, xmax = 1e+05)
Arguments
o
Discrete powerlaw object.
g
A guess on the true value of the lower bound.
c
Confidence on the guess. A value between 1 and 100. By default is set to 90.
k
Number of computations after a local minimum in the KS statistics is reached.
xmax
Max value considered in the estimation of the lower bound.
References
A. Bessi, Speeding up lower bound estimation in powerlaw distributions, arXiv
getXmin2
5
Examples
x = moby
o = displo(x)
est = getXmin(o)
getXmin2
Lower bound estimator for discrete powerlaw distributions
Description
Lower bound estimator for discrete powerlaw distributions based on the distances between probability mass functions.
Usage
getXmin2(o, g = 1, c = 90, k = 5, xmax = 1e+05)
Arguments
o
Discrete powerlaw object.
g
A guess on the true value of the lower bound.
c
Confidence on the guess. A value between 1 and 100. By default is set to 90.
k
Number of computations after a local minimum in the KS statistics is reached.
xmax
Max value considered in the estimation of the lower bound.
References
A. Bessi, Speeding up lower bound estimation in powerlaw distributions, arXiv
Examples
x = moby
o = displo(x)
est = getXmin2(o)
6
len
inspect
Inspect Discrete Powerlaw Distributions
Description
A graphical tool to inspect discrete powerlaw distributions.
Usage
inspect(o, plot = TRUE, guess = 1, showQ = FALSE, plothill = TRUE,
summary = TRUE, xmax = 1e+05)
Arguments
o
A discrete powerlaw object.
plot
Logical, whether to show the plot. By default is set to TRUE.
guess
A guess on the true value of the lower bound. By default is set to 1.
showQ
Logical, whether to show the quantiles of the distribution. By default is set to
FALSE.
plothill
Logical, whether to show Hill plot. By default is set to TRUE.
summary
Logical, whether to print some information about the powerlaw distribution. By
default is set to TRUE.
xmax
The maximum value to consider as candidate for the lower bound.
Examples
x = moby
o = displo(x)
inspection = inspect(o, guess = 7)
len
Length of a Vector
Description
Length function for lazy people.
Usage
len(x)
Arguments
x
A vector.
MAE
7
Examples
x = moby
n = len(x)
Mean Absolute Error
MAE
Description
Mean Absolute Error.
Usage
MAE(x, y)
Arguments
x,y
Two vectors of the same length.
Examples
x = runif(10)
y = runif(10)
MAE(x,y)
MAPE
Mean Absolute Percentage Error
Description
Mean Absolute Percentage Error.
Usage
MAPE(x, y)
Arguments
x,y
Examples
x = runif(10)
y = runif(10)
MAPE(x,y)
Two vectors of the same length.
8
MPE
Moby Dick word count
moby
Description
The frequency of occurrence of unique words in the novel Moby Dick by Herman Melville.
Usage
moby
Format
A vector.
Source
M. E. J. Newman, Power laws, Pareto distributions and Zipf’s law. Contemporary Physics 46, 323
(2005)
Mean Percentage Error
MPE
Description
Mean Percentage Error.
Usage
MPE(x, y)
Arguments
x,y
Examples
x = runif(10)
y = runif(10)
MPE(x,y)
Two vectors of the same length.
MSE
9
Mean Squared Error
MSE
Description
Mean Squared Error.
Usage
MSE(x, y)
Arguments
x,y
Two vectors of the same length.
Examples
x = runif(10)
y = runif(10)
MSE(x,y)
pdispl
Discrete Powerlaw Distribution Function
Description
Complementary cumulative distribution function for the discrete power law distribution with parameters xmin and alpha.
Usage
pdispl(q, xmin, alpha, lower.tail = TRUE)
Arguments
q
Vector of quantiles.
xmin
The lower bound of the powerlaw distribution.
alpha
The scaling parameter.
lower.tail
Logical, whether is returned the cumulative distribution function insted of the
complementary cumulative distribution function. By default is set to TRUE.
Examples
x = rdispl(n = 1e4, xmin = 10, alpha = 2.5)
pdispl(x, xmin = 10, alpha = 2.5, lower.tail = TRUE)
10
plothill
plotfit
Plot Fit of Discrete Powerlaw Distributions
Description
Plot fit of discrete powerlaw distributions.
Usage
plotfit(o, xmax = 1e+05)
Arguments
o
A discrete powerlaw object.
xmax
The maximum value to show.
Examples
x = moby
o = displo(x)
getXmin(o)
plotfit(o)
plothill
Hill plot
Description
Hill plot for discrete power law distributions.
Usage
plothill(o, gxmin = 0, xmax = 1e+05)
Arguments
o
A discrete powerlaw object.
gxmin
Guess on the true value of the lower bound.
xmax
Maximum value considered as candidate for the lower bound. Default is set to
1e5.
Examples
x = moby
o = displo(x)
plothill(o)
plotmultifit
plotmultifit
11
Plot Multiple Fit of Discrete Powerlaw Distributions
Description
Plot multiple fit of discrete powerlaw distributions.
Usage
plotmultifit(o)
Arguments
o
A discrete powerlaw object.
Examples
x = moby
o = displo(x)
getXmin(o)
plotmultifit(o)
plotols
Plot OLS Fit of Discrete Powerlaw Distributions
Description
Plot OLS fit of discrete powerlaw distributions.
Usage
plotols(o)
Arguments
o
Examples
x = moby
o = displo(x)
plotols(o)
A discrete powerlaw object.
12
rdispl
pmf
Probability Mass Function
Description
Empirical Probability Mass Function.
Usage
pmf(x)
Arguments
x
A vector of observations.
Examples
x = rdispl(n = 1e4, xmin = 10, alpha = 2.5, xmax = 1e5)
obs = pmf(x)$x
probs = pmf(x)$y
rdispl
Discrete Powerlaw Random Generator
Description
Random generator of discrete power law distribution with parameters xmin and alpha.
Usage
rdispl(n, xmin, alpha, xmax = 1e+05)
Arguments
n
Number of observations.
xmin
The lower bound of the powerlaw distribution.
alpha
The scaling parameter.
xmax
The maximum value generated.
Examples
x = rdispl(n = 1e4, xmin = 10, alpha = 2.5, xmax = 1e5)
RMSE
13
Root Mean Squared Error
RMSE
Description
Root Mean Squared Error.
Usage
RMSE(x, y)
Arguments
x,y
Two vectors of the same length.
Examples
x = runif(10)
y = runif(10)
RMSE(x,y)
std
Unity-based Normalization
Description
Unity-based normalization of a vector.
Usage
std(x)
Arguments
x
Examples
x = moby
z = std(x)
A vector to normalize.
Index
∗Topic absolute
MAE, 7
MAPE, 7
∗Topic bound
getXmin, 4
getXmin2, 5
∗Topic complementary
ddispl, 3
pdispl, 9
∗Topic cumulative
cdf, 2
data_cdf, 2
pdispl, 9
∗Topic datasets
moby, 8
∗Topic data
data_cdf, 2
∗Topic density
ddispl, 3
∗Topic discrete
ddispl, 3
displo, 3
getXmin, 4
getXmin2, 5
pdispl, 9
rdispl, 12
∗Topic distributions
inspect, 6
plotfit, 10
plotmultifit, 11
plotols, 11
std, 13
∗Topic distribution
cdf, 2
data_cdf, 2
ddispl, 3
pdispl, 9
∗Topic empirical
cdf, 2
data_cdf, 2
pmf, 12
∗Topic error
MAE, 7
MAPE, 7
MPE, 8
MSE, 9
RMSE, 13
∗Topic estimator
getXmin, 4
getXmin2, 5
∗Topic fit
plotfit, 10
plotmultifit, 11
plotols, 11
std, 13
∗Topic function
cdf, 2
data_cdf, 2
ddispl, 3
pdispl, 9
pmf, 12
∗Topic generator
rdispl, 12
∗Topic hill
plothill, 10
∗Topic inspect
inspect, 6
∗Topic length
len, 6
∗Topic lower
getXmin, 4
getXmin2, 5
∗Topic mass
pmf, 12
∗Topic mean
MAE, 7
MAPE, 7
MPE, 8
14
INDEX
MSE, 9
RMSE, 13
∗Topic of
data_cdf, 2
∗Topic percentage
MAPE, 7
MPE, 8
∗Topic plot
plotfit, 10
plothill, 10
plotmultifit, 11
plotols, 11
std, 13
∗Topic powerlaw
ddispl, 3
displo, 3
getXmin, 4
getXmin2, 5
inspect, 6
pdispl, 9
plotfit, 10
plotmultifit, 11
plotols, 11
rdispl, 12
std, 13
∗Topic probability
pmf, 12
∗Topic random
rdispl, 12
∗Topic root
RMSE, 13
∗Topic squared
MSE, 9
RMSE, 13
∗Topic vector
len, 6
cdf, 2
data_cdf, 2
ddispl, 3
displo, 3
fastsum, 4
getXmin, 4
getXmin2, 5
inspect, 6
15
len, 6
MAE, 7
MAPE, 7
moby, 8
MPE, 8
MSE, 9
pdispl, 9
plotfit, 10
plothill, 10
plotmultifit, 11
plotols, 11
pmf, 12
rdispl, 12
RMSE, 13
std, 13