Maxwell Speed Distribution - Averages

Averages

There are three candidates for what is called the "average" value of the speed of the Maxwell speed distribution.

Firstly, by finding the maximum of the MSD (by differentiating, setting the derivative equal to zero and solving for the speed), we can determine the most probable speed. Calling this vmp, we find that:

Second, we can find the mean value of v from the MSD. Calling this :

Third and finally, we can find the root mean square of the speed by finding the expected value of v2. (Alternatively, and much simpler, we can solve it by using the equipartition theorem.) Calling this vrms:

Notice that

These are three different ways of defining the average velocity, and they are not numerically the same. It is important to be clear about which quantity is being used.

Probability distributions
Discrete univariate with finite support
  • Benford
  • Bernoulli
  • Beta-binomial
  • binomial
  • categorical
  • hypergeometric
  • Poisson binomial
  • Rademacher
  • discrete uniform
  • Zipf
  • Zipf-Mandelbrot
Discrete univariate with infinite support
  • beta negative binomial
  • Boltzmann
  • Conway–Maxwell–Poisson
  • discrete phase-type
  • Delaporte
  • extended negative binomial
  • Gauss–Kuzmin
  • geometric
  • logarithmic
  • negative binomial
  • parabolic fractal
  • Poisson
  • Skellam
  • Yule–Simon
  • zeta
Continuous univariate supported on a bounded interval, e.g.
  • Arcsine
  • ARGUS
  • Balding-Nichols
  • Bates
  • Beta
  • Beta rectangular
  • Irwin–Hall
  • Kumaraswamy
  • logit-normal
  • Noncentral beta
  • raised cosine
  • triangular
  • U-quadratic
  • uniform
  • Wigner semicircle
Continuous univariate supported on a semi-infinite interval, usually [0,∞)
  • Benini
  • Benktander 1st kind
  • Benktander 2nd kind
  • Beta prime
  • Bose–Einstein
  • Burr
  • chi-squared
  • chi
  • Coxian
  • Dagum
  • Davis
  • Erlang
  • exponential
  • F
  • Fermi–Dirac
  • folded normal
  • Fréchet
  • Gamma
  • generalized inverse Gaussian
  • half-logistic
  • half-normal
  • Hotelling's T-squared
  • hyper-exponential
  • hypoexponential
  • inverse chi-squared (scaled inverse chi-squared)
  • inverse Gaussian
  • inverse gamma
  • Kolmogorov
  • Lévy
  • log-Cauchy
  • log-Laplace
  • log-logistic
  • log-normal
  • Maxwell–Boltzmann
  • Maxwell speed
  • Mittag–Leffler
  • Nakagami
  • noncentral chi-squared
  • Pareto
  • phase-type
  • Rayleigh
  • relativistic Breit–Wigner
  • Rice
  • Rosin–Rammler
  • shifted Gompertz
  • truncated normal
  • type-2 Gumbel
  • Weibull
  • Wilks' lambda
Continuous univariate supported on the whole real line (−∞, ∞)
  • Cauchy
  • exponential power
  • Fisher's z
  • generalized normal
  • generalized hyperbolic
  • geometric stable
  • Gumbel
  • Holtsmark
  • hyperbolic secant
  • Landau
  • Laplace
  • Linnik
  • logistic
  • noncentral t
  • normal (Gaussian)
  • normal-inverse Gaussian
  • skew normal
  • slash
  • stable
  • Student's t
  • type-1 Gumbel
  • variance-gamma
  • Voigt
Continuous univariate with support whose type varies
  • generalized extreme value
  • generalized Pareto
  • Tukey lambda
  • q-Gaussian
  • q-exponential
  • shifted log-logistic
Mixed continuous-discrete univariate distributions
  • rectified Gaussian
Multivariate (joint)
Discrete
Ewens
multinomial
Dirichlet-multinomial
negative multinomial
Continuous
Dirichlet
Generalized Dirichlet
multivariate normal
Multivariate stable
multivariate Student
normal-scaled inverse gamma
normal-gamma
Matrix-valued
inverse matrix gamma
inverse-Wishart
matrix normal
matrix t
matrix gamma
normal-inverse-Wishart
normal-Wishart
Wishart
Directional
Univariate (circular) directional
Circular uniform
univariate von Mises
wrapped normal
wrapped Cauchy
wrapped exponential
wrapped Lévy
Bivariate (spherical)
Kent
Bivariate (toroidal)
bivariate von Mises
Multivariate
von Mises–Fisher
Bingham
Degenerate and singular
Degenerate
discrete degenerate
Dirac delta function
Singular
Cantor
Families
  • Circular
  • compound Poisson
  • elliptical
  • exponential
  • natural exponential
  • location-scale
  • maximum entropy
  • mixture
  • Pearson
  • Tweedie
  • wrapped

Read more about this topic:  Maxwell Speed Distribution

Other articles related to "averages, average":

Avrage - Miscellaneous Types
... Other more sophisticated averages are trimean, trimedian, and normalized mean, with their generalizations ... One can create one's own average metric using the generalized f-mean where f is any invertible function ... generating means is not general enough to capture all averages ...
Rating Scales Used Online - Qualitative Description
... when aggregated statistics such as averages are used for lists and rankings of products ... While it is not uncommon to calculate averages or means for such data, doing so cannot be justified because in calculating averages, equal intervals are ... scales commonly used online are as follow Averages should not be calculated for data of the kind collected ...
List Of Australian TV News Presenters Year By Year - Weekly News Averages 2010
... NFA= no figures available Market Week 1 Weeknight News Averages ABC News Seven News Nine News Ten News SBS World News 5 Cities 930,000 1,310,000 1,134,000 823,000 NFA Sydney 240,000 316,000 316,000 ...