Generating Gamma-Distributed Noise Sequences with Implementation Approaches

This article presents methodologies for generating gamma-distributed noise sequences and analyzing various parameters of Gaussian noise. To generate gamma-distributed noise sequences, the implementation involves three key steps: First, utilize a random number generator to create a uniformly distributed random number sequence (commonly implemented using functions like rand() in MATLAB or random.random() in Python). Second, apply the inverse transform sampling method to convert uniformly distributed random numbers into gamma-distributed random numbers - this requires computing the inverse cumulative distribution function (CDF) of the gamma distribution. Finally, perform comprehensive analysis on the resulting noise sequence using statistical measures. For analyzing Gaussian noise parameters, researchers can employ methods such as least squares estimation and maximum likelihood estimation (MLE). These techniques typically involve optimizing parameter values to best fit the observed data, with MLE implementation requiring probability density function calculations and optimization algorithms like gradient descent. These analytical approaches enable researchers to gain deeper insights into noise signal characteristics, thereby providing fundamental support for signal processing applications and communication system design.