How to use this calculator
Enter numeric observations and choose a candidate distribution. Inspect the Q–Q plot and binned observed versus fitted counts.
Formula and method
Normal MLE μ̂=mean, σ̂²=Σ(x−mean)²/n. Exponential MLE λ̂=1/mean. JB=n[skew²+(kurtosis−3)²/4]/6.
Worked example
A symmetric sample has skew near zero; a small Jarque–Bera p-value flags deviation in skew or kurtosis.
Assumptions and supported scope
Normal or exponential fits, 8–1000 observations. Q–Q and descriptive KS D; normal Jarque–Bera asymptotic p-value only. No Shapiro–Wilk or calibrated KS/Lilliefors p-value, no automatic model selection or censoring.
Method references
Method and worked example checked against the calculator implementation. About our methods · Report a correction