Statistics Calculators

Available Statistical Tools

Use our interactive statistical calculators for data analysis and mathematical statistics

Beginner

Event Relations & Probability Calculator

Calculate event probabilities, unions, intersections, conditional probabilities, and independence relationships

Features:

Classical probability calculations
Event unions & intersections
Conditional probability
Independence testing
Bayes' theorem applications
Step-by-step solutions

Beginner to Intermediate

Bernoulli Model & Binomial Calculator

Calculate binomial probabilities, expected values, variance, and probability distributions for Bernoulli trials

Features:

Binomial probability calculations
Expected value & variance
Binomial coefficients
Probability distributions
Statistical measures
Interactive examples

Beginner

Descriptive Statistics Calculator

Calculate mean, median, mode, standard deviation, and other descriptive measures for your sample data

Features:

Mean, median, mode
Variance & standard deviation
Quartiles & percentiles
Skewness & kurtosis
Mathematical formulas
Statistical interpretation

Intermediate

Distribution Transformation Calculator

Transform between different probability distributions (Gamma ↔ Exponential, Chi-square, etc.)

Features:

Gamma to Exponential conversion
Gamma to Chi-square conversion
F to Beta/Z distribution
Parameter transformation
Mathematical formulas
Real-world applications

Intermediate

Confidence Interval Calculator

Calculate confidence intervals for normal population means using pivotal quantity method

Features:

Normal population mean intervals
Known/unknown variance scenarios
Pivotal quantity method
Step-by-step solutions
Critical value references
Interactive explanations

Intermediate

Hypothesis Testing Calculator

Perform statistical hypothesis tests for normal population parameters with step-by-step solutions

Features:

U-test and t-test for means
Chi-square test for variance
Two-sided and one-sided tests
P-value calculations
Critical value comparisons
Statistical decision making

Intermediate

Nonparametric Testing Calculator

Distribution-free statistical tests including sign tests, rank-based methods, and goodness-of-fit tests

Features:

Sign test for medians
Wilcoxon rank sum test
Chi-square goodness-of-fit
Independence testing
Robust to outliers
No distributional assumptions

Intermediate

Bayesian Prior Distribution Calculator

Calculate prior distribution parameters using moments method, quantiles method, or expert knowledge for Bayesian analysis

Features:

Beta prior parameter calculation
Gamma prior parameter estimation
Normal prior specification
Moments method implementation
Quantiles method approach
Prior sensitivity analysis

Intermediate

Bayesian Posterior Calculator

Calculate posterior distributions and Bayesian estimates using conjugate priors with sample data integration

Features:

Beta-Binomial conjugacy
Gamma-Poisson conjugacy
Normal-Normal conjugacy
Posterior mean estimation
Posterior variance calculation
Step-by-step derivations

Intermediate

Bayesian Credible Intervals Calculator

Calculate Bayesian credible intervals using posterior distributions with different interval types and interpretations

Features:

Equal-tail credible intervals
Highest posterior density intervals
Single-sided credible bounds
Distribution transformation methods
Chi-square distribution applications
Bayesian uncertainty quantification

Intermediate

Bayesian Prediction Calculator

Calculate posterior predictive distributions for future observations using Bayesian methodology and uncertainty propagation

Features:

Posterior predictive density
Bernoulli prediction analysis
Poisson prediction modeling
Normal prediction intervals
Parameter uncertainty integration
Decision-theoretic applications

Available Statistical Tools

Use our interactive statistical calculators for data analysis and mathematical statistics

Intermediate to Advanced

Multi-Step Transition Calculator

Calculate n-step transition probabilities using Chapman-Kolmogorov equations and matrix powers

Features:

Matrix power computation
Chapman-Kolmogorov equations
Multi-step probabilities
Interactive matrix input
Step-by-step calculations
Validation & verification

Intermediate to Advanced

Stationary Distribution Calculator

Calculate equilibrium probabilities and long-term behavior of Markov chains using balance equations

Features:

Balance equation solving
Linear system solution
Equilibrium analysis
Convergence verification
Solution validation
Mathematical proofs

Advanced

Gambler's Ruin Calculator

Analyze absorption probabilities and expected game durations for random walk problems

Features:

Fair & unfair game analysis
Ruin probability calculation
Expected duration computation
Visual probability display
Mathematical formulas
Real-world applications

Available Statistical Tools

Use our interactive statistical calculators for data analysis and mathematical statistics

Intermediate

Poisson Increment Probability Calculator

Calculate P{N(t) - N(s) = k} for homogeneous Poisson processes with step-by-step solutions

Features:

Increment probability calculation
Poisson distribution
Interactive parameter input
Step-by-step solutions
Mathematical formulas
Real-world applications

Intermediate to Advanced

Poisson Event Time Calculator

Calculate W_n probability density and distribution function for event occurrence times

Features:

Event time calculations
Gamma distribution
Probability density
Distribution function
Interactive examples
Mathematical foundation

Intermediate

Poisson Time Interval Calculator

Calculate T_n probability density and distribution function for time intervals

Features:

Time interval analysis
Exponential distribution
Memoryless property
Distribution functions
Interactive calculations
Real-world examples

Intermediate to Advanced

Homogeneous Poisson Process Calculator

Calculate increment probabilities, event occurrence times, and time intervals for Poisson processes

Features:

Increment probability calculation
Event timing distributions
Time interval analysis
Gamma & exponential distributions
Interactive parameter input
Step-by-step solutions

Available Statistical Tools

Use our interactive statistical calculators for data analysis and mathematical statistics

Advanced

Brownian Motion Calculator

Calculate standard Brownian motion properties: linear combinations, covariance, first passage time, and maximum value probability

Features:

Linear combination calculations
Covariance analysis
First passage time probability
Maximum value distribution
Reflection principle
Interactive examples

Advanced

Brownian Bridge Calculator

Calculate Brownian bridge process properties: covariance, variance, and boundary conditions

Features:

Covariance calculation
Variance analysis
Boundary conditions
Fixed-end processes
Interactive calculations
Mathematical foundation

Advanced

Geometric Brownian Motion Calculator

Calculate general Brownian motion and geometric Brownian motion properties: increment distribution and expected price

Features:

General BM calculations
Geometric BM modeling
Expected price calculation
Drift & diffusion effects
Financial applications
Interactive examples

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