truncated_normal_paper_2014_fsu

truncated_normal_paper_2014_fsu, "The Truncated Normal Distribution", an informal technical report which describes the truncated normal distribution, which is a modification of the normal distribution that uses a finite value for one or both endpoints of the domain. This makes it possible to sensibly and efficiently describe phenomena whose variation from the mean value is typically normal, but which does not vary infinitely far or must not be so modeled, for physical or mathematical reasons. This paper was written at Florida State University, in 2014.

Information about the truncated normal distribution is presented, including the derivation from the normal distribution, the mathematical formulas for the probability density function (PDF), and cumulative density function (CDF), the four parameters generally needed, the inversion of the CDF and how to efficiently sample the distribution, the computation of quadrature rules, product quadrature rules, and sparse grid quadrature rules.

• truncated_normal_paper_2014_fsu.tex
• truncated_normal_paper_2014_fsu.pdf

Files:

• erf_plot.png, a plot of the error function ERF.
• gh_sequence.png, an indexed family of Gauss-Hermite rules.
• he_plot.png, a plot of the first five Hermite polynomials.
• hermite_o7.png, the grid for the 7 point Gauss-Hermite quadrature rule.
• hermite_o7x7.png, the grid for the 7x7 point Gauss-Hermite product rule.
• normal_cdf_plot.png, a plot of the standard normal cumulative density function.
• normal_histogram.png, a histogram that approximates the normal PDF.
• normal_icdf_plot.png, a plot of the inverse of the standard normal cumulative density function.
• normal_pdf_plot.png, a plot of the standard normal probability density function.
• sparsel1_grid.png, the 5 point level 1 Gauss-Hermite sparse grid in 2D.
• sparsel2_grid.png, the 17 point level 2 Gauss-Hermite sparse grid in 2D.
• tnp_plot1.png, truncated normal distribution #1.
• tnp_plot2.png, truncated normal distribution #2.
• tnp_plot3.png, truncated normal distribution #3.
• tnp_plot4.png, truncated normal distribution #4.