feat: Added Exponential Probability Distribution (TheAlgorithms#2780)

* Add Exponential Distribution

* Modified the documentation

* Update Documentation

* Update probability/exponential_dist.cpp

Co-authored-by: realstealthninja <[email protected]>

* Update probability/exponential_dist.cpp

Co-authored-by: realstealthninja <[email protected]>

* Update probability/exponential_dist.cpp

Co-authored-by: realstealthninja <[email protected]>

* Update the files

* Removed the link from documentation

* docs: remove the second brief tag

* Update latex notation

Co-authored-by: realstealthninja <[email protected]>

* Update latex notation

Co-authored-by: realstealthninja <[email protected]>

* Corrected format issues

* Update probability/exponential_dist.cpp

Co-authored-by: realstealthninja <[email protected]>

* Update probability/exponential_dist.cpp

Co-authored-by: realstealthninja <[email protected]>

* Update probability/exponential_dist.cpp

Co-authored-by: realstealthninja <[email protected]>

* Added more test, formatted with clang-format

* Update files

* Update format issues

* Add more tests

* Added namespaces

---------

Co-authored-by: realstealthninja <[email protected]>

Author: HarshilShah1804

probability/exponential_dist.cpp

@@ -0,0 +1,151 @@
+/**
+ * @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 assert
+#include <cmath>      // For std::pow
+#include <iostream>   // For I/O operation
+#include <stdexcept>  // For std::invalid_argument
+#include <string>     // For std::string
+
+/**
+ * @namespace probability
+ * @brief Probability algorithms
+ */
+namespace probability {
+/**
+ * @namespace exponential_dist
+ * @brief Functions for the [Exponential
+ * Distribution](https://en.wikipedia.org/wiki/Exponential_distribution)
+ * algorithm implementation
+ */
+namespace geometric_dist {
+/**
+ * @brief the expected value of the exponential distribution
+ * @returns \f[\mu = \frac{1}{\lambda}\f]
+ */
+double exponential_expected(double lambda) {
+    if (lambda <= 0) {
+        throw std::invalid_argument("lambda must be greater than 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) {
+        throw std::invalid_argument("lambda must be greater than 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) {
+        throw std::invalid_argument("lambda must be greater than 0");
+    }
+    return 1 / lambda;
+}
+}  // namespace geometric_dist
+}  // namespace probability
+
+/**
+ * @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;
+
+    double lambda_4 = 0;     // Test 0
+    double lambda_5 = -2.3;  // Test negative value
+
+    const float threshold = 1e-3f;
+
+    std::cout << "Test for lambda = 1 \n";
+    assert(
+        std::abs(expected_1 - probability::geometric_dist::exponential_expected(
+                                  lambda_1)) < threshold);
+    assert(std::abs(var_1 - probability::geometric_dist::exponential_var(
+                                lambda_1)) < threshold);
+    assert(std::abs(std_1 - probability::geometric_dist::exponential_std(
+                                lambda_1)) < threshold);
+    std::cout << "ALL TEST PASSED\n\n";
+
+    std::cout << "Test for lambda = 2 \n";
+    assert(
+        std::abs(expected_2 - probability::geometric_dist::exponential_expected(
+                                  lambda_2)) < threshold);
+    assert(std::abs(var_2 - probability::geometric_dist::exponential_var(
+                                lambda_2)) < threshold);
+    assert(std::abs(std_2 - probability::geometric_dist::exponential_std(
+                                lambda_2)) < threshold);
+    std::cout << "ALL TEST PASSED\n\n";
+
+    std::cout << "Test for lambda = 3 \n";
+    assert(
+        std::abs(expected_3 - probability::geometric_dist::exponential_expected(
+                                  lambda_3)) < threshold);
+    assert(std::abs(var_3 - probability::geometric_dist::exponential_var(
+                                lambda_3)) < threshold);
+    assert(std::abs(std_3 - probability::geometric_dist::exponential_std(
+                                lambda_3)) < threshold);
+    std::cout << "ALL TEST PASSED\n\n";
+
+    std::cout << "Test for lambda = 0 \n";
+    try {
+        probability::geometric_dist::exponential_expected(lambda_4);
+        probability::geometric_dist::exponential_var(lambda_4);
+        probability::geometric_dist::exponential_std(lambda_4);
+    } catch (std::invalid_argument& err) {
+        assert(std::string(err.what()) == "lambda must be greater than 0");
+    }
+    std::cout << "ALL TEST PASSED\n\n";
+
+    std::cout << "Test for lambda = -2.3 \n";
+    try {
+        probability::geometric_dist::exponential_expected(lambda_5);
+        probability::geometric_dist::exponential_var(lambda_5);
+        probability::geometric_dist::exponential_std(lambda_5);
+    } catch (std::invalid_argument& err) {
+        assert(std::string(err.what()) == "lambda must be greater than 0");
+    }
+    std::cout << "ALL TEST PASSED\n\n";
+}
+
+/**
+ * @brief Main function
+ * @return 0 on exit
+ */
+int main() {
+    test();  // Self test implementation
+    return 0;
+}