feat: Added Exponential Probability Distribution

probability/exponential_dist.cpp

@@ -0,0 +1,103 @@
+/**
+ * @file
+ * @brief [Exponential
+ * Distribution](https://en.wikipedia.org/wiki/Exponential_distribution)
+ *
+ * The exponential distribution is used to model
+ * events occuring between a Poisson process like radioactive decay.
+ *
+ * \f[P(x, \lambda) = \lambda e^{-\lambda x}\f]
+ *
+ * Summary of variables used:
+ * \f$\lambda\f$ : rate parameter
+ */
+
+#include <cassert>   // For asserting the test cases
+#include <cmath>     // For power function
+#include <iostream>  // For I/O operation
+
+/**
+ * @brief the expected value of the exponential distribution
+ * @returns \f[\mu = \frac{1}{\lambda}\f]
+ */
+double exponential_expected(double lambda) {
+    if (lambda <= 0) {
+        std::cout << "Error: Lambda must be greater than 0." << '\n';
+        assert(lambda > 0);
+    }
+    return 1 / lambda;
+}
+
+/**
+ * @brief the variance of the exponential distribution
+ * @returns \f[\sigma^2 = \frac{1}{\lambda^2}\f]
+ */
+double exponential_var(double lambda) {
+    if (lambda <= 0) {
+        std::cout << "Error: Lambda must be greater than 0." << '\n';
+        assert(lambda > 0);
+    }
+    return 1 / pow(lambda, 2);
+}
+
+/**
+ * @brief the standard deviation of the exponential distribution
+ * @returns \f[\sigma = \frac{1}{\lambda}\f]
+ */
+double exponential_std(double lambda) {
+    if (lambda <= 0) {
+        std::cout << "Error: Lambda must be greater than 0." << '\n';
+        assert(lambda > 0);
+    }
+    return 1 / lambda;
+}
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    double lambda_1 = 1;
+    double expected_1 = 1;
+    double var_1 = 1;
+    double std_1 = 1;
+
+    double lambda_2 = 2;
+    double expected_2 = 0.5;
+    double var_2 = 0.25;
+    double std_2 = 0.5;
+
+    double lambda_3 = 3;
+    double expected_3 = 0.333333;
+    double var_3 = 0.111111;
+    double std_3 = 0.333333;
+
+    const float threshold = 1e-3f;
+
+    std::cout << "Test for lambda = 1 \n";
+    assert(std::abs(expected_1 - exponential_expected(lambda_1)) < threshold);
+    assert(std::abs(var_1 - exponential_var(lambda_1)) < threshold);
+    assert(std::abs(std_1 - exponential_std(lambda_1)) < threshold);
+    std::cout << "ALL TEST PASSED\n\n";
+
+    std::cout << "Test for lambda = 2 \n";
+    assert(std::abs(expected_2 - exponential_expected(lambda_2)) < threshold);
+    assert(std::abs(var_2 - exponential_var(lambda_2)) < threshold);
+    assert(std::abs(std_2 - exponential_std(lambda_2)) < threshold);
+    std::cout << "ALL TEST PASSED\n\n";
+
+    std::cout << "Test for lambda = 3 \n";
+    assert(std::abs(expected_3 - exponential_expected(lambda_3)) < threshold);
+    assert(std::abs(var_3 - exponential_var(lambda_3)) < threshold);
+    assert(std::abs(std_3 - exponential_std(lambda_3)) < threshold);
+    std::cout << "ALL TEST PASSED\n";
+}
+
+/**
+ * @brief Main function
+ * @return 0 on exit
+ */
+int main() {
+    test();  // Self test implementation
+    return 0;
+}