Opusmodus 3.0.28933 Update

[opmo]

ver. 3.0.28933

 

New functions:

 

Probability->Distribution

BETA-DISTRIBUTION

The function returns a list of values generated from the Beta distribution using the given alpha and beta parameters. The Beta distribution is a continuous probability distribution defined on the interval [0, 1]. It is commonly used to model random variables that have values between zero and one, such as proportions, probabilities, or parameters that are constrained to a specific range.

BILATERAL-EXPONENTIAL

The bilateral exponential distribution is a probability distribution that models random variables with values in a symmetric interval around zero. It is often used to describe quantities that exhibit both positive and negative values, such as the differences between two related measurements or errors in scientific experiments. The function returns a list of values generated from the bilateral exponential distribution using the given lower limits a and upper limits b.

CAUCHY-DISTRIBUTION

The Cauchy distribution is a probability distribution that is characterized by its symmetric bell-shaped curve. The function returns a list of values generated from the Cauchy distribution using the given location parameters x0 and scale parameters gamma. It is also known as the Cauchy-Lorentz distribution and is named after mathematicians Augustin Cauchy and Hendrik Lorentz. Applications of the Cauchy distribution include modeling extreme events, analyzing data with outliers, and in physics, where it arises naturally in certain physical phenomena, such as quantum mechanics and resonant systems.

GAUSSIAN-DISTRIBUTION

The function returns a list of pairs (x, y), where x and y are random numbers generated from a Gaussian distribution with the given means and standard deviations. The Gaussian distribution, also known as the normal distribution or bell curve, is one of the most widely used probability distributions in statistics. It is named after mathematician Carl Friedrich Gauss.

WEIBULL-DISTRIBUTION

The Weibull distribution is a probability distribution that is commonly used to model the failure times or lifetimes of various types of systems or phenomena. It was introduced by Wallodi Weibull, a Swedish engineer and mathematician. The function returns a list of values generated from the Weibull distribution using the given scale parameters lambda and shape parameters k.

 

Mathematics->Interpolation

SEGMENT-INTERPOLATION

This function interpolates over segments defined by time, value, and an exponent using either linear or cosine interpolation. It creates a segment for each time point with the corresponding value and exponent. It then generates a sequence of points, for each of which it determines the appropriate segment. For a point, it finds the two segments it falls between and applies the appropriate interpolation based on the exponent of the first segment. If there is no subsequent segment, the function simply returns the value of the first segment. If the point falls exactly on the time of a segment, no interpolation is necessary and the function directly returns the corresponding value.

 

Best wishes,

Janusz