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The width of the sloped parts corresponds to the width of the narrowest uniform distribution. If the uniform distributions have the same width w, the result is a triangular distribution , symmetric about its mean, on the support [a+c,a+c+2w].
Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum ...
The shape of a distribution will fall somewhere in a continuum where a flat distribution might be considered central and where types of departure from this include: mounded (or unimodal), U-shaped, J-shaped, reverse-J shaped and multi-modal. [1] A bimodal distribution would have two high points rather than one. The shape of a distribution is ...
This distribution for a = 0, b = 1 and c = 0.5—the mode (i.e., the peak) is exactly in the middle of the interval—corresponds to the distribution of the mean of two standard uniform variables, that is, the distribution of X = (X 1 + X 2) / 2, where X 1, X 2 are two independent random variables with standard uniform distribution in [0, 1]. [1]
The distribution of a random variable that is defined as the minimum of several random variables, each having a different Weibull distribution, is a poly-Weibull distribution. The Weibull distribution was first applied by Rosin & Rammler (1933) to describe particle size distributions.
The spacing between each sampling (i.e. the distance between pixels measuring the data) is uniform. The peak is "well-sampled", so that less than 10% of the area or volume under the peak (area if a 1D Gaussian, volume if a 2D Gaussian) lies outside the measurement region.
Unlike a probability, a probability density function can take on values greater than one; for example, the continuous uniform distribution on the interval [0, 1/2] has probability density f(x) = 2 for 0 ≤ x ≤ 1/2 and f(x) = 0 elsewhere.
The problem of estimating the maximum of a discrete uniform distribution on the integer interval [,] from a sample of k observations is commonly known as the German tank problem, following the practical application of this maximum estimation problem, during World War II, by Allied forces seeking to estimate German tank production.