stamp-valuation-probability-model

How to use statistics just provide confidence in an estimate of a large lot value.

Overview

This repository contains a Python script to estimate the value of a stamp collection using statistical analysis and a logistic distribution. The script performs the following tasks:

Calculates descriptive statistics for a sample of pages from the stamp collection.
Determines the confidence level for the sample.
Uses a logistic function to model the distribution of stamp values.
Estimates the total number of stamps and the total value of the collection based on the sample data and the logistic distribution.

Requirements

Python 3.x
NumPy
SciPy
Matplotlib

Installation

Clone the repository:

git clone https://github.com/your-username/stamp-price-probability-model.git
cd stamp-price-probability-model

Install the required Python packages:

pip install numpy scipy matplotlib

Usage

Run the script to perform the analysis and estimate the value of the stamp collection:

python3 stamp_price_model.py

Python Script: stamp_price_model.py

import numpy as np
from scipy.stats import norm
import matplotlib.pyplot as plt

# Function to generate logistic distribution
def logistic_function(x, L=1, x0=0.25, k=10):
    return L / (1 + np.exp(-k * (x - x0)))

# Generate logistic distribution values
x_values = np.linspace(0, 2, 1000)
y_values = logistic_function(x_values, L=1, x0=0.15, k=10)

# Normalize to make it a probability distribution
y_values = y_values / np.sum(y_values)

# Plot the distribution
plt.plot(x_values, y_values)
plt.title('Adjusted Logistic Distribution of Stamp Values')
plt.xlabel('Value ($)')
plt.ylabel('Probability Density')
plt.grid(True)
plt.show()

# Simulate stamp values based on logistic distribution
np.random.seed(42)
n_stamps = 10000
stamp_values = np.random.choice(x_values, size=n_stamps, p=y_values)

# Calculate expected value per stamp
expected_value_per_stamp = np.mean(stamp_values)

# Sample data
sample_data = np.array([16,18,20,4,26,7,23,5,0,6,2,14,53,4,12,32,15,11,0,0,0,0,7,7,0,2,2,31])

# Descriptive statistics
mean_sample = np.mean(sample_data)
std_sample = np.std(sample_data, ddof=1)  # using ddof=1 for sample standard deviation

# Parameters for confidence interval calculation
N = 192  # total number of pages
n = len(sample_data)  # sample size
margin_of_error = 5  # desired margin of error

# Calculate Z-score for current sample size and margin of error
finite_population_correction = np.sqrt((N - n) / (N - 1))
standard_error = std_sample / np.sqrt(n) * finite_population_correction
Z = margin_of_error / standard_error

# Calculate confidence level from Z-score
confidence_level = norm.cdf(Z) * 2 - 1  # two-tailed test

# Estimating total number of stamps
estimated_total_stamps = mean_sample * N

# Estimating total value of the collection
estimated_total_value = estimated_total_stamps * expected_value_per_stamp

# Output the results
print(f"Sample Mean: {mean_sample}")
print(f"Sample Standard Deviation: {std_sample}")
print(f"Sample Size: {n}")
print(f"Confidence Level: {confidence_level * 100:.2f}%")
print(f"Mean number of stamps per sampled page: {mean_sample}")
print(f"Estimated total number of stamps: {estimated_total_stamps}")
print(f"Expected value per stamp: {expected_value_per_stamp}")
print(f"Estimated total value of the collection: {estimated_total_value}")