Math Module

rmath.stats

Descriptive and inferential statistics. All functions accept list[float] or rmath.Vector. Uses Welford's algorithm for numerically stable single-pass computations.

example.py

import rmath as rm

data = [2.4, 3.1, 2.8, 3.5, 2.9, 3.2]
report = rm.stats.describe(data)
# {'count': 6, 'mean': 2.98, 'variance': 0.14, ...}

t, p = rm.stats.t_test_independent(sample_a, sample_b)

Descriptive Statistics

Function	Returns	Description
`sum(data)`	float	Arithmetic sum
`mean(data)`	float	Arithmetic mean (NaN for empty)
`median(data)`	float	Median via O(N) selection
`mode(data)`	float	Most frequent value
`variance(data)`	float	Sample variance (ddof=1)
`std_dev(data)`	float	Sample standard deviation
`skewness(data)`	float	Fisher-Pearson skewness
`kurtosis(data)`	float	Excess kurtosis (Fisher)
`iqr(data)`	float	Interquartile range (Q3 − Q1)
`mad(data)`	float	Median absolute deviation
`describe(data)`	dict	Full summary: count, mean, variance, std, skewness, kurtosis

Inferential Statistics

Function	Returns	Description
`correlation(x, y)`	float	Pearson correlation coefficient
`covariance(x, y)`	float	Sample covariance
`spearman_correlation(x, y)`	float	Spearman rank correlation
`t_test_independent(a, b)`	(t_stat, p_value)	Welch's T-test for two samples
`anova_oneway(groups)`	(F, df_between, df_within)	One-way ANOVA across groups

Regression

Function	Returns	Description
`linear_regression(x, y)`	dict	Returns `{'slope', 'intercept', 'r_squared'}`

Distributions

Normal(mu, sigma)

`.pdf(x)`	Probability density
`.cdf(x)`	Cumulative distribution
`.ppf(x)`	Percent-point function (inverse CDF)
`.mean()`	Distribution mean

StudentT(location, scale, freedom)

.pdf(x) · .cdf(x) · .ppf(x)

Poisson(lambda_)

`.pmf(k)`	Probability mass function
`.cdf(k)`	Cumulative distribution

Exponential(rate)

.pdf(x) · .cdf(x) · .ppf(x)