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