dxxx(x,) returns the density or the value on the y-axis of a probability distribution for a discrete value of x pxxx(q,) returns the cumulative density function (CDF) or the area under the curve to ...

Interest Rate Probability Distributions Implied by Derivatives Prices is a daily measure of the distribution of future short-term interest rates, calculated from prices of fixed-income derivatives ...

Probability underpins AI, cryptography and statistics. However, as the philosopher Bertrand Russell said, “Probability is the most important concept in modern science, especially as nobody has the ...

Predicting how complex stochastic systems respond to small external perturbations is central in physics, climate science, and engineering. We combine the generalized fluctuation–dissipation theorem ...

Life is uncertain. None of us know what is going to happen. We know little of what has happened in the past or is happening now outside our immediate experience. Uncertainty has been called the ...

The mathematician Daniel Litt has driven social media users to distraction with a series of simple-seeming but counterintuitive probability puzzles. In late January, Daniel Litt posed an innocent ...

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

Once you have a basic understanding of sports betting odds, it’s easy to determine the favorite or underdog in a game and the favored option among a range of choices. You can also go a step further by ...

TensorFlow Probability is a library for probabilistic reasoning and statistical analysis in TensorFlow. As part of the TensorFlow ecosystem, TensorFlow Probability provides integration of ...

It has been known for a long time that (1) when graphs of income amount on income relative rank for two income distributions intersect twice, three “transfer groups” are generated, with the poorest ...