Statistics Functions (38)

Perform a one-way ANOVA (Analysis of Variance) F-test comparing means across multiple groups.

Create a Beta distribution with shape parameters alpha and beta. Returns an object with pdf(x), cdf(x), mean, and variance.

Create a binomial distribution with n trials and success probability p. The binomial distribution models the number of successes in n independent trials. Returns an object with pmf(k), cdf(k), mean, and variance.

Perform a chi-squared test. For 1D arrays (observed, expected), performs a goodness-of-fit test.

Create a chi-squared distribution with k degrees of freedom. Commonly used in hypothesis testing and confidence interval estimation for variance. Returns an object with pdf(x), cdf(x), mean, and variance.

Compute the correlation coefficient of a two list with values, For matrices, the matrix correlation coefficient is calculated.

Compute the sample covariance of two datasets. cov(x, y) = sum((x_i - mean_x) * (y_i - mean_y)) / (n - 1)

Compute the cumulative sum of all values.

Create an exponential distribution with rate parameter lambda. Models the time between events in a Poisson process. Returns an object with pdf(x), cdf(x), icdf(p), mean, and variance.

Create an F-distribution with numerator df1 and denominator df2 degrees of freedom. Returns an object with pdf(x), cdf(x), mean, and variance.

Create a Gamma distribution with shape k and rate beta. Returns an object with pdf(x), cdf(x), mean, and variance.

Compute a frequency histogram. If bins is a number, creates that many equal-width bins from min to max. If bins is an array, uses those values as bin edges. Returns an object with counts, binEdges, and binCenters.

Perform a Kolmogorov-Smirnov test. One-sample: compare a sample ECDF to a theoretical CDF function.

Compute the sample excess kurtosis of a dataset. Kurtosis measures the "tailedness" of the probability distribution. A normal distribution has excess kurtosis of 0.

Perform simple linear regression (ordinary least squares) on two datasets. Returns an object with slope, intercept, r (correlation coefficient), r2 (R-squared), and predict(x) function.

Create a log-normal distribution with log-scale parameters mu and sigma. Returns an object with pdf(x), cdf(x), icdf(p), mean, and variance.

Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.

Perform a Mann-Whitney U test (Wilcoxon rank-sum test), a non-parametric test for whether

Compute the maximum value of a list of values. If any NaN values are found, the function yields the last NaN in the input.

Compute the arithmetic mean of a list of values.

Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.

Compute the minimum value of a list of values. If any NaN values are found, the function yields the last NaN in the input.

Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.

Compute the simple moving average of a dataset with a given window size. Returns an array of length (n - window + 1).

Create a normal (Gaussian) distribution with mean mu and standard deviation sigma. Returns an object with pdf(x), cdf(x), icdf(p), mean, and variance.

Create a Poisson distribution with rate parameter lambda. The Poisson distribution models the number of events in a fixed interval. Returns an object with pmf(k), cdf(k), mean, and variance.

Perform Principal Component Analysis (PCA). Centers the data, computes the covariance matrix,

Compute the product of all values.

Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probability are: Number, BigNumber. \n\nIn case of a (multi dimensional) array or matrix, the

Perform the Shapiro-Wilk test for normality. Sorts the sample and computes W using

Compute the sample skewness of a dataset. Skewness measures the asymmetry of the probability distribution. Uses the adjusted Fisher-Pearson standardized moment coefficient.

Compute the standard deviation of all values, defined as std(A) = sqrt(variance(A)). Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".

Perform a two-sample Welch t-test (unequal variances). Tests whether the means of two independent samples differ significantly. Uses the Welch-Satterthwaite approximation for degrees of freedom. Returns an object with t (statistic), df (degrees of freedom), and pValue (two-tailed).

Compute the sum of all values.

Create a continuous uniform distribution on [a, b]. Returns an object with pdf(x), cdf(x), icdf(p), mean, and variance.

Compute the variance of all values. Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".

Create a Weibull distribution with shape parameter k and scale parameter lambda. Generalizes the exponential distribution (k=1 reduces to exponential with rate 1/lambda). Returns an object with pdf(x), cdf(x), mean, and variance.