TATITIC CALCULATOR
Shannon Entropy
A precise tool.
What is the Shannon Entropy & How does it work?
Shannon entropy measures the average amount of information produced by a stochastic source of data. It quantifies the uncertainty inherent in a set of possible outcomes, making it a cornerstone of information theory and many statistical applications.
For a discrete random variable with probabilities (p_1, p_2, dots, p_n), the entropy is calculated using the following formula:
H = -sum_{i=1}^{n} p_i log_{2} p_i
p_i = probability of the i‑th outcome
Higher entropy indicates a more uniform distribution of probabilities, meaning each outcome is less predictable. Conversely, lower entropy reflects a distribution where some outcomes dominate, reducing overall uncertainty.
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Frequently Asked Questions
What is Shannon entropy?
Shannon entropy measures the average amount of information produced by a stochastic source, quantifying the uncertainty in possible outcomes.
How do I calculate Shannon entropy for a discrete random variable?
Use the formula H = -∑(p_i * log₂ p_i) where p_i is the probability of the i-th outcome.
What does higher entropy indicate?
Higher entropy indicates a more uniform distribution of probabilities, meaning outcomes are less predictable.
Can Shannon entropy be negative?
No, Shannon entropy cannot be negative. It is always non-negative and equals zero when there is no uncertainty (i.e., one outcome has probability 1).
What is the base of the logarithm in Shannon entropy?
The base of the logarithm in Shannon entropy is 2, which gives the result in bits.
How is Shannon entropy used in information theory?
Shannon entropy is fundamental in information theory to quantify the amount of uncertainty or information in a message or data source.
Can I use this calculator for continuous random variables?
This calculator is designed for discrete random variables. For continuous variables, you would need to use differential entropy instead.
Results are for informational purposes only and do not constitute professional advice.