brnldist 1.0.0

Generate Bernoulli distributed values using Linear Congruential Generator (LCG)

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📌 Description

Generate Bernoulli Distributed Values using Linear Congruential Generator (LCG)

brnldist is a lightweight Python package that simulates Bernoulli-distributed random variables using values generated by a Linear Congruential Generator (LCG).

It combines the simplicity of LCG for pseudo-random number generation with a Bernoulli distribution threshold to produce a sequence of 0s and 1s.

This is useful for simulations, basic statistical modeling, or understanding how pseudo-random processes work behind random variable generation.

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⚙️ How It Works

1. Uses LCG to generate a sequence of pseudo-random integers:

   $$ X_{n+1} = (a \cdot X_n + c) \mod m $$

2. Normalizes each LCG value to the interval [0, 1] by dividing by the modulus m.

3. Compares each normalized value with a probability threshold p:

   • If the value < p → return 1 (success)
   • Else → return 0 (failure)

4. Returns a sequence of binary outcomes following a Bernoulli(p) distribution.

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📈 Example Output

from brnldist import brnldist
from brnldist import lcg
a=2
c=3
x0=5
m=103
p=0.5
n=10
y, u, x = lcg(a, c, x0, m, p, n)

#Parameters:
        #a (int): LCG multiplier
        #c (int): LCG increment
        #x0 (int): Seed value
        #m (int): LCG modulus
        #p (float): Bernoulli threshold (0 to 1)
        #n (int): Number of values to generate
print("LCG raw values (y):", y)
print("Normalized values (u):", u)
print("Second normalized value u[1]",u[1])
print("Bernoulli output (x):", x)

# y = LCG raw values
# u = normalized values
# u[1] = Second normalized value
# x = Bernoulli (0 or 1) outcomes

👤 Author Rohit Kumar Behera 📧 Email: [e-mail] 🌐 GitHub: github.com/muinrohit 🏠 Location: Odisha, India

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