kimau / lua-stats

Statistical functions for Lua

Lua-Stats

Statistical functions for Lua

Reference

Generic Functions

Function	Description
integral(f, start, stop, delta, ...)	Calculates the area under a function f from start to stop in delta-sized steps. The optional arguments ... are passed on to the function to integrate
integralUntil(f, a, start = 0, delta = 0.001, ...)	Integrates a function f from start at delta steps until the absolute area is a
factorial(x)	Calculates the factorial recursively for integer x or using the gamma function if x is a float
findX(y, f, accuracy = 0.001, ...)	Finds the x needed for f to return y at a certain accuracy, given the optional arguments ...
gamma(x)	the probability density function of the gamma distribution for x
beta(x,y)	The probability density function of the beta distibution
pValue(q, f, ...)	Calculates the p-value of a test statistic coming from the CDF f. The optional arguments ... are passed on to f.
map(t, f)	Applies a function f to every value of a table t.
reduce(t, f)	Reduces a table t using a function f that takes two arguments.
in_table(value, t, key = false)	True if value is in table t. Searches for a key if key is true
unify(...)	Takes an arbitrary number of values and tables and concatenates them into one big table
unique(t)	Returns unique entities in table t
multiSubscript(i, ...)	Returns an Array containing all elements of the provided tables at key i

Arithmetic functions

All functions taking only arbitrary optional arguments ... concatenate all supplied values into a table and calculate from that.

Function	Description
sum(...)	Sum
count(...)	Count of values
mean(...)	Average of values
sumSquares(...)	Sum of the squared difference from the mean
var(...)	Variance
varPop(...)	Variance for the population
sd(...)	Standard deviation
sdPop(...)	Standard Deviation for the population
cov(t1, t2)	Returns the Covariance between tables t1 and t1
cor(t1, t2, method = "Pearson")	Returns the correlaion between two arrays t1 and t2
min(...)	Minimum value
max(...)	Maximum value
frequency(t)	Returns the number of occurrences of each element in a table t
sdPooled(sd1, n1, sd2, n2)	Calculates the pooled standard deviation
quantile(t, q)	Gets the q-th quantile of sequence t, where 0 >= t >= 1
median(t)	Median for table t
quartile(t, i)	Wrapper for quantile returning 0: Minimum 1: 1st quartile 2: Median 3: 3rd quartile 4: Maximum

Normal Distribution Functions

Function	Description
dNorm(x, mu = 0, sd = 1)	Probability density function for the normal distribution with mean mu and standard deviation sd at point x
pNorm(x, mu = 0, sd = 0, accuracy = 0.001)	Cumulative distribution function for the Normal distribution with mean mu and standard deviation sd at point x
qNorm(q, accuracy = 0.01)	Calculates the z-value for q for N(0

T-distribution functions

Function	Description
dT(x, df)	probability density function of the t-distribution at x with df degrees of freedom
pT(q, df, accuracy = 0.01)	CDF of the d-distribution at x with df degrees of freedom
qT(p, df)	t-value corresponding to the p-value provided at df degrees of freedom

Chi-square distribution functions

Function	Description
dChisq(x, df)	Probability density function of the chi-square distribution at x with df degrees of freedom.
pChisq(q, df)	CDF of the chi-square distribution at q with df degrees of freedom
qChisq(p, df, accuracy = 0.01)	Chi square value corresponding to the p value provided at df degrees of freedom down to accuracy's accuracy.

F distribution functions

Function	Description
dF(x, df1, df2)	Probability density function of x at df1 and df2 degrees of freedom.
pF(x, df1, df2)	CDF of the F distribution of x at df1 and df2 degrees of freedom.
qF(p, df1, df2, accuracy = 0.01)	F-statistic corresponding to the p-value at df1 and df2 degrees of freedom.

Tests

Function	Description
assertTables(...)	Asserts that all provided arguments are tables
zValue(y1, sd1, n1 [, y2, sd2, n2, sameVar = false])	Performs a z-test on one or two means
zTest(t1, t2, sameVar = false)	Performs a z-test on two sequences of numbers t1 and t2
zTestP(t1, t2, sameVar = false)	Returns the p-value of a z-test on t1 and t2
tValue(y1, sd1, n1 [, y2, sd2, n2, sameVar = false])	Performs a t-test on one or two means.
tTest(t1, t2, sameVar = false)	Returns the t-value of the comparison of t1 against t2
tTestP(t1, t2, sameVar = false)	Returns the p-value of the t-statistic of the comparison of t1 against t2
fValue(s1, s2)	Returns the F-value of two variances s1 and s2
fTest(t1, t2)	Returns the F-value of the comparison of t1 against t2
fTestP(t1, t2)	Returns the p-value of the F-statistic of the comparison of t1 against t2