Addons/stats/base/univariate
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stats/base/univariate - Univariate statistics
mean v arithmetic mean (dyadic: weighted) geomean v geometric mean harmean v harmonic mean commonmean v common mean dev v deviation from mean (dyadic: weighted) ssdev v sum of squared deviations (dyadic: weighted) var v sample variance (dyadic: weighted) stddev v standard deviation (dyadic: weighted) varp v population variance stddevp v population standard deviation min v minimum max v maximum midpt v index of midpoint median v median quantiles v returns the quantile of y at the specified probabilities x nquantiles v returns the values which partition y into x quantiles iqr v calculates the interquartile range (IQR) of y ntiles v assign values of y to x quantiles cile v assign values of y to x subsets of nearly equal size rankOrdinal a ordinal ranking ("0 1 2 3") of array y rankCompete a standard competition ranking ("0 0 2 3") of array y rankDense a dense ranking ("0 0 1 2") of array y rankFractional a fractional ranking ("0 1.5 1.5 3") of array y dstat v descriptive statistics freqcount v frequency count Idotr v equivalent to I. but intervals closed on left, open on right histogram v tally of the items in each bin binnedData a Applies verb u to the values of y after binning them in the intervals specified by x kurtosis v 4th moment coefficient skewness v 3rd moment coefficient
mean
mean (v) arithmetic mean (dyadic: weighted)
geomean
geomean (v) geometric mean
harmean
harmean (v) harmonic mean
commonmean
commonmean (v) common mean
dev
dev (v) deviation from mean (dyadic: weighted)
ssdev
ssdev (v) sum of squared deviations (dyadic: weighted)
var
var (v) sample variance (dyadic: weighted)
stddev
stddev (v) standard deviation (dyadic: weighted)
"p" suffix = population definitions
varp
varp (v) population variance
stddevp
stddevp (v) population standard deviation
min
min (v) minimum
max
max (v) maximum
midpt
midpt (v) index of midpoint
median
median (v) median
quantiles
quantiles (v) returns the quantile of y at the specified probabilities x
y is: numeric values to calculate quantiles for x is: 0{:: probabilities at which to calculate quantiles (default 0.25 0.5 0.75) 1{:: method for calculating quantiles (default 7) EG: 0 0.25 0.5 0.75 1 quantiles 2 4 5 6 7 8 9
NB. There are a number of different methods for calculating quantiles
NB. https://en.wikipedia.org/wiki/Quantile , also Hyndman and Fan (1996)
qh4=. 4 : 'x * # y' NB. alpha=0, beta=1
qh5=. 4 : '0.5 + x * # y' NB. alpha=0.5, beta=0.5
qh6=. 4 : 'x * >:@# y' NB. alpha=0, beta=0
qh7=. 4 : '1 + x * <:@# y' NB. alpha=1, beta=1 ; default for R, NumPy & Julia
qh8=. 4 : '1r3 + x * 1r3 + # y' NB. alpha=1/3, beta=1/3 ; recommended by Hyndman and Fan (1996)
qh9=. 4 : '3r8 + x * 0.25 + # y' NB. alpha=3/8, beta=3/8 ; tends to be used for Normal QQ plots
Qh=: (qh4 f.)`(qh5 f.)`(qh6 f.)`(qh7 f.)`(qh8 f.)`(qh9 f.)
QuantileMethod=: 7 NB. default quantile method to use
nquantiles
nquantiles (v) returns the values which partition y into x quantiles
returns 1 less value than the number of quantiles specified y is: numeric values to calculate quantiles for x is: number of quantiles (default 4) EG: 4 nquantiles 2 4 5 6 7 8 9
iqr
iqr (v) calculates the interquartile range (IQR) of y
ntiles
ntiles (v) assign values of y to x quantiles
x is: number of quantiles (default 4) EG: 2 ntiles 2 4 5 6 7 8 9
cile
cile (v) assign values of y to x subsets of nearly equal size
eg: 3 cile i.12
rankOrdinal
rankOrdinal (a) ordinal ranking ("0 1 2 3") of array y
tied items are ranked on the order they appear in y eg: /: rankOrdinal 5 2 5 0 6 2 4 NB. rank ascending eg: \: rankOrdinal 5 2 5 0 6 2 4 NB. rank descending
rankCompete
rankCompete (a) standard competition ranking ("0 0 2 3") of array y
eg: /: rankCompete 5 2 5 0 6 2 4 NB. rank ascending eg: \: rankCompete 5 2 5 0 6 2 4 NB. rank descending
rankDense
rankDense (a) dense ranking ("0 0 1 2") of array y
eg: /: rankDense 5 2 5 0 6 2 4 NB. rank ascending eg: \: rankDense 5 2 5 0 6 2 4 NB. rank descending
rankFractional
rankFractional (a) fractional ranking ("0 1.5 1.5 3") of array y
Items with the same ranking have the mean of their ordinal ranks. eg: /: rankFractional 5 2 5 0 6 2 4 NB. rank ascending eg: \: rankFractional 5 2 5 0 6 2 4 NB. rank descending
dstat
dstat (v) descriptive statistics
table of formatted descriptive statistics
freqcount
freqcount (v) frequency count
(value, frequency) sorted by decreasing frequency
Idotr
Idotr (v) Equivalent to I. but intervals are closed on the left and open on the right
Idotr : (0{x) <= y < (1{x) I. : (0{x) < y <= (1{x)
histogram
histogram (v) histogram
x is a list of interval start/end points. The number of intervals is 1+#x y is an array of data The result is a list of counts of the number of data points in each interval.
binnedData
binnedData (a) Applies verb u to the values of y after binning them in the intervals specified by x
x is a list of interval start/end points. The number of intervals is 1+#x y is an array of data. eg: < binnedData NB. verb to box the binned data eg: (+/ % #) binnedData NB. verb to average the binned data
kurtosis
kurtosis (v) 4th moment coefficient
skewness
skewness (v) 3rd moment coefficient