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Statistics Calculators

Statistics Calculators

Comprehensive collection of statistical calculators for data analysis, hypothesis testing, and mathematical statistics

Interactive ToolsData AnalysisStatistical Inference

Statistical Calculators Available!

Start analyzing your data with our available statistical calculators including descriptive statistics, hypothesis testing, and nonparametric methods!

Descriptive StatisticsHypothesis TestingNonparametric TestsConfidence Intervals

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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