Extreme Value Distribution

Visualize Gumbel distribution for alignment scores and understand P-values in BLAST

0.267
0.041
32.6530
E-value
1.0000
P-value
23.9
Bit Score
63.1
Characteristic (u)
500.0M
Search Space
Extreme Value Distribution (Gumbel):
P(Score ≥ S) = 1 - exp(-E)
E = K × m × n × e^(-λS)

Current Parameters:
E = 0.041 × 500 × 1.0M × e^(-0.267 × 50)
E = 32.6530

Probability Density Function

What is Extreme Value Distribution?

The Extreme Value Distribution (Gumbel) describes the distribution of maximum values from random samples. In BLAST, optimal alignment scores follow this distribution, not a normal distribution, allowing accurate P-value and E-value calculations.

How to Use This Visualizer

Explore EVD parameters and their effects:

  1. Adjust λ and K parameters
  2. Set sequence lengths and score threshold
  3. View different distribution representations

When to Use

This tool is useful when you need to:

  • Understand BLAST E-value calculations
  • Visualize score significance thresholds
  • Compare EVD with normal distribution

Example Input

Typical BLOSUM62 parameters:

λ = 0.267, K = 0.041
Query: 500 aa
Database: 1M residues
Score: 50

E-value ≈ 0.006 (highly significant)

Example Output

Statistical measures:

E-value: 0.006
P-value: 0.006
Bit Score: 42.8
Significance: p < 0.01

Score unlikely by chance alone.

FAQ

Q: Why not use normal distribution?
A: Maximum scores from many comparisons follow EVD, which has a longer tail than normal distribution.

Q: What is characteristic value u?
A: The score where E-value = 1, calculated as u = ln(Kmn)/λ.