A Student’s t continuous random variable.
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As an instance of the
rv_continuous
class, t
object inherits from ita collection of generic methods (see below for the full list),and completes them with details specific for this particular distribution.Notes
The probability density function for
t
is:[f(x, nu) = frac{Gamma((nu+1)/2)} {sqrt{pi nu} Gamma(nu/2)} (1+x^2/nu)^{-(nu+1)/2}]
where (x) is a real number and the degrees of freedom parameter(nu) (denoted
df
in the implementation) satisfies(nu > 0). (Gamma) is the gamma function(scipy.special.gamma
).![Battery Stats V1 1 1 Battery Stats V1 1 1](https://cdn.instructables.com/FDU/Z5AN/I1MQ4KV8/FDUZ5ANI1MQ4KV8.LARGE.jpg?auto=webp&frame=1&height=300)
The probability density above is defined in the “standardized” form. To shiftand/or scale the distribution use the
loc
and scale
parameters.Specifically, t.pdf(x,df,loc,scale)
is identicallyequivalent to t.pdf(y,df)/scale
withy=(x-loc)/scale
.Examples
Calculate a few first moments:
Display the probability density function (
pdf
):Alternatively, the distribution object can be called (as a function)to fix the shape, location and scale parameters. This returns a “frozen”RV object holding the given parameters fixed.
Freeze the distribution and display the frozen
pdf
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Check accuracy of
cdf
and ppf
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Generate random numbers:
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And compare the histogram:
Methods
rvs(df, loc=0, scale=1, size=1, random_state=None) | Random variates. |
pdf(x, df, loc=0, scale=1) | Probability density function. |
logpdf(x, df, loc=0, scale=1) | Log of the probability density function. |
cdf(x, df, loc=0, scale=1) | Cumulative distribution function. |
logcdf(x, df, loc=0, scale=1) | Log of the cumulative distribution function. |
sf(x, df, loc=0, scale=1) | Survival function (also defined as 1-cdf , but sf is sometimes more accurate). |
logsf(x, df, loc=0, scale=1) | Log of the survival function. |
ppf(q, df, loc=0, scale=1) | Percent point function (inverse of cdf — percentiles). |
isf(q, df, loc=0, scale=1) | Inverse survival function (inverse of sf ). |
moment(n, df, loc=0, scale=1) | Non-central moment of order n |
stats(df, loc=0, scale=1, moments=’mv’) | Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). |
entropy(df, loc=0, scale=1) | (Differential) entropy of the RV. |
fit(data) | Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments. |
expect(func, args=(df,), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds) | Expected value of a function (of one argument) with respect to the distribution. |
median(df, loc=0, scale=1) | Median of the distribution. |
mean(df, loc=0, scale=1) | Mean of the distribution. |
var(df, loc=0, scale=1) | Variance of the distribution. |
std(df, loc=0, scale=1) | Standard deviation of the distribution. |
Macos winclone. interval(alpha, df, loc=0, scale=1) | Endpoints of the range that contains alpha percent of the distribution |
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