The triangular distribution is commonly used in simulations, risk analysis, and probabilistic modeling. It is defined by a lower limit, upper limit, and a mode, representing the most likely value. Use this calculator to compute probabilities and visualize the distribution.
P(X = ):
P(X < ):
P(X ≤ ):
P(X > ):
P(X ≥ ):
Mean:
Median:
Variance:
Understanding the Triangular Distribution
The Triangular Distribution is a continuous probability distribution defined by a lower limit, an upper limit, and a mode, which represents the most likely value. It is commonly used in simulations and risk analysis.
Key Components of the Triangular Distribution
- Lower Limit (a): The minimum possible value.
- Upper Limit (b): The maximum possible value.
- Mode (c): The most likely value in the distribution.
Formula for Triangular Distribution
The probability density function (PDF) for the triangular distribution is given by:
Step-by-Step Example
Let's assume the lower limit is \(a = 1\), the upper limit is \(b = 10\), and the mode is \(c = 5\). If we want to find the probability for \(x = 4\), we apply the formula above.
Mean, Median, and Variance
- Mean (μ): \( \frac{a + b + c}{3} \)
- Median: If \( c \leq \frac{a + b}{2} \), the median is \( a + \sqrt{(b-a)(c-a)/2} \). Otherwise, the median is \( b - \sqrt{(b-a)(b-c)/2} \).
- Variance (σ²): \( \frac{a^2 + b^2 + c^2 - ab - ac - bc}{18} \)
Further Reading
Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.