Gumbel Maximum Distribution
Evaluate a Gumbel maximum distribution’s cumulative probability, median and variance.
ProbabilityOpen tool ↗THE FEUTEX TOOLKIT
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Beta Distribution Moments
Inspect a beta distribution’s mean, variance and skewness on the unit interval.
ProbabilityOpen tool ↗Gamma Distribution Moments
Inspect a gamma distribution’s mean, variance, skewness and excess kurtosis using shape and scale.
ProbabilityOpen tool ↗Poisson Event Window
Estimate the probabilities of no events, one event or multiple events in a constant-rate window.
ProbabilityOpen tool ↗Wilson Proportion Interval
Calculate a Wilson score confidence interval for a proportion from successes and trials.
StatisticsOpen tool ↗Mean Confidence Interval from Summary
Construct a mean confidence interval from summary statistics and a supplied t critical value.
StatisticsOpen tool ↗Mean Precision Sample Size
Estimate the sample count needed for a target mean-estimation precision with known variability.
StatisticsOpen tool ↗Welch Two-Sample Test Statistic
Calculate Welch’s two-sample statistic and approximate degrees of freedom from group summaries.
StatisticsOpen tool ↗Paired Difference Test Statistic
Calculate a paired-sample test statistic from the mean and standard deviation of paired differences.
StatisticsOpen tool ↗Pooled Standardized Mean Difference
Compare group means in pooled-standard-deviation units using two independent sample summaries.
StatisticsOpen tool ↗Merge Two Sample Summaries
Combine two disjoint sample summaries into one count, mean and sample variance.
StatisticsOpen tool ↗Correlation Fisher Interval
Construct an approximate Fisher-transformed confidence interval for a Pearson correlation.
StatisticsOpen tool ↗Two-Group Event Association
Compare two groups using risk ratio, risk difference, odds ratio and log-odds uncertainty.
StatisticsOpen tool ↗2×2 Independence Statistic
Calculate Pearson’s independence statistic and signed association for a two-by-two count table.
StatisticsOpen tool ↗McNemar Paired Discordance
Inspect corrected and uncorrected McNemar statistics from paired discordant outcomes.
StatisticsOpen tool ↗Binary Classification Scorecard
Evaluate precision, recall, specificity, F1 and Matthews correlation from a binary confusion matrix.
StatisticsOpen tool ↗Binary Rater Agreement
Compare observed agreement with chance agreement and calculate Cohen’s kappa for two binary raters.
StatisticsOpen tool ↗Binary Entropy Profile
Calculate uncertainty, perplexity and success information for a Bernoulli probability.
ProbabilityOpen tool ↗Hoeffding Mean Deviation Bound
Bound sample-mean deviations for independent observations with known finite limits.
ProbabilityOpen tool ↗Weight Effective Sample Size
Estimate weight-based effective sample size and efficiency from sums of weights and squared weights.
StatisticsOpen tool ↗Process Capability Indices
Compare a stable process with specification limits using Cp, Cpk and one-sided capability indices.
StatisticsOpen tool ↗Adjusted R-Squared and Residual Scale
Adjust regression R-squared for predictor count and calculate residual scale and degrees of freedom.
StatisticsOpen tool ↗Likelihood Information Criteria
Calculate AIC, small-sample AICc and BIC from a fitted model’s likelihood and parameter count.
StatisticsOpen tool ↗One-Way ANOVA Summary
Build one-way ANOVA statistics and effect size from between-group and within-group sums of squares.
StatisticsOpen tool ↗Two-Proportion Z Statistic
Calculate the pooled large-sample z statistic comparing two independent event proportions.
StatisticsOpen tool ↗Multiple-Testing Error Budget
Allocate a family-wise error budget and adjust one p-value using Bonferroni’s method.
StatisticsOpen tool ↗Sampling Without Replacement
Estimate the mean, variance and feasible success range when sampling without replacement.
ProbabilityOpen tool ↗Trials until Multiple Successes
Estimate trial count and variability required to reach multiple independent successes.
ProbabilityOpen tool ↗Lognormal Moment Profile
Find a lognormal model’s median, mean, variance and mode from natural-log parameters.
ProbabilityOpen tool ↗Correlated Measurement Uncertainty
Propagate correlated standard uncertainties through a sum, difference and product.
StatisticsOpen tool ↗No-Fixed-Point Assignment Count
Count assignments with no item in its original position and calculate their random-permutation probability.
ProbabilityOpen tool ↗Balanced Parenthesis Structure Count
Count valid balanced-parenthesis sequences and equivalent ordered binary tree shapes.
MathOpen tool ↗Ordered and Unordered Selections
Count selections without replacement with and without regard to ordering.
MathOpen tool ↗Birthday Collision Estimate
Estimate collision probability and expected matching pairs for independent draws from equal-probability categories.
ProbabilityOpen tool ↗Coupon Collection Expectation
Calculate the expected draw count and variance needed to collect every uniformly distributed coupon type.
ProbabilityOpen tool ↗Random Bin Occupancy
Estimate occupied, empty and singleton bins after independent uniform assignments.
ProbabilityOpen tool ↗Sphere Intersection Volume
Measure the shared volume and intersection-circle radius of two partially overlapping spheres.
GeometryOpen tool ↗Cone Solid Angle and Sphere Fraction
Calculate a cone aperture’s solid angle and the fraction of a sphere it covers.
GeometryOpen tool ↗Helix Path Profile
Measure a circular helix’s length, rise, curvature and torsion from radius, pitch and turns.
GeometryOpen tool ↗Triangle from Two Sides and Included Angle
Solve a triangle’s remaining side, angles and area from two sides and their included angle.
GeometryOpen tool ↗Plane Angle and Intersection Direction
Find the acute angle between planes and a direction vector for their intersection line.
GeometryOpen tool ↗Quadrilateral Coordinate Survey
Calculate signed area and perimeter from four consecutive boundary coordinates.
GeometryOpen tool ↗Great-Circle Distance
Measure the shortest spherical surface route and straight chord between two latitude-longitude positions.
GeometryOpen tool ↗Reflect a Point across a Plane
Mirror a three-dimensional point across a plane given by its coefficients.
GeometryOpen tool ↗Nearest Point on a Line Segment
Find the nearest point on a finite line segment, including endpoint cases.
GeometryOpen tool ↗Circle through Three Points
Locate the center and radius of the unique circle passing through three noncollinear points.
GeometryOpen tool ↗Runge–Kutta Four-Stage Step
Combine four correctly evaluated Runge–Kutta stage slopes into one fourth-order solution step.
MathOpen tool ↗Cubic Polynomial Evaluation
Evaluate a cubic polynomial, its first two derivatives and its signed integral from zero.
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