stats
T-Distribution
Student's t-distribution — PDF, CDF, p-value, critical t±, CI bounds, normal overlay; handles df 1–1000.
Parameters
Degrees of freedom df
t value
Tail
Confidence level (for critical t)
Overlay
Results
PDF f(t)—
CDF P(T ≤ t)—
p-value (tail)—
Critical t* (95% two-tailed)—
95% CI bounds—
Mean—
Variance df/(df−2)—
Excess kurtosis 6/(df−4)—
CDF via I_x(df/2, 0.5), x = df/(df+t²) · Lentz CF, max 200 iter
As df→∞, T(df) → N(0,1) · heavier tails for small df
As df→∞, T(df) → N(0,1) · heavier tails for small df