  Experimental data in Particle and Nuclear physics, Particle Astrophysics and
Radiation Protection Dosimetry are obtained from experimental facilities
comprising a complex array of sensors, electronics and software. Computer
simulation is used to study the measurement process. Probability Density
Functions (PDFs) of measured physical parameters deviate from true PDFs due to
resolution, bias, and efficiency effects. Good estimates of the true PDF are
necessary for testing theoretical models, comparing results from different
experiments, and combining results from various research endeavors. In the
article, the histogram method is employed to estimate both the measured and
true PDFs. The binning of histograms is determined using the K-means clustering
algorithm. The true PDF is estimated through the maximization of the likelihood
function with entropy regularization, utilizing a non-linear optimization
algorithm specially designed for this purpose. The accuracy of the results is
assessed using the Mean Integrated Square Error. To determine the optimal value
for the regularization parameter, a bootstrap method is applied. Additionally,
a mathematical model of the measurement system is formulated using system
identification methods. This approach enhances the robustness and precision of
the estimation process, providing a more reliable analysis of the system's
characteristics.
