Statistical functions for Lua
| 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 |
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 |
| 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 |
| 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 |
| 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. |
| 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. |
| 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 |