Poisson point processIn probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field.
Exponential distributionIn probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.
Compound Poisson processA compound Poisson process is a continuous-time stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of the jumps is also random, with a specified probability distribution. To be precise, a compound Poisson process, parameterised by a rate and jump size distribution G, is a process given by where, is the counting variable of a Poisson process with rate , and are independent and identically distributed random variables, with distribution function G, which are also independent of When are non-negative integer-valued random variables, then this compound Poisson process is known as a stuttering Poisson process.
Erlang distributionThe Erlang distribution is a two-parameter family of continuous probability distributions with support . The two parameters are: a positive integer the "shape", and a positive real number the "rate". The "scale", the reciprocal of the rate, is sometimes used instead. The Erlang distribution is the distribution of a sum of independent exponential variables with mean each. Equivalently, it is the distribution of the time until the kth event of a Poisson process with a rate of .
NitrogenNitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at seventh in total abundance in the Milky Way and the Solar System. At standard temperature and pressure, two atoms of the element bond to form N2, a colorless and odorless diatomic gas. N2 forms about 78% of Earth's atmosphere, making it the most abundant uncombined element in air.
