Description Usage Arguments Details Value Author(s) References See Also Examples
int_lap
computes the error interval of a set of residuals
assuming a Laplace distribution with zero location for the noise.
int_gau
computes the error interval of a set of residuals
assuming a Gaussian distribution with zero mean for the noise.
int_lap_mu
computes the error interval of a set of residuals
assuming a Laplace distribution.
int_gau_mu
computes the error interval of a set of residuals
assuming a Gaussian distribution.
int_beta
computes the error interval of a set of residuals
assuming a Beta distribution.
int_weibull
computes the error interval of a set of residuals
assuming a Weibull distribution.
See also 'Details'.
int_moge
computes the error interval of a set of residuals
assuming a MOGE distribution.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | int_lap(phi, s)
int_gau(phi, s, ps = 0, threshold = 10^-2, upper = 10^6)
int_lap_mu(phi, s, ps = stats::median(phi, na.rm = T), threshold = 10^-2,
upper = 10^6)
int_gau_mu(phi, s, ps = mean(phi, na.rm = T), threshold = 10^-2,
upper = 10^6)
int_beta(phi, s, original_phi = phi, ps = 10^-4, threshold = 10^-4,
upper = 1, m1 = mean(phi, na.rm = T), m2 = mean(phi^2, na.rm = T),
alpha_0 = (m1 * (m1 - m2))/(m2 - m1^2), beta_0 = (alpha_0 * (1 - m1)/m1))
int_weibull(phi, s, ps = 10^-4, threshold = 10^-2, upper = 10^6,
k_0 = 1)
int_moge(phi, s, ps = 10^-4, threshold = 10^-4, upper = 10^6,
lambda_0 = 1, alpha_0 = 1, theta_0 = 1)
|
phi |
residual values used to compute the error interval. |
s |
confidence level, e,g. s=0.05 for the standard 95 percent confidence interval. |
ps |
minimum value to search for solution of the integral equation to solve. See also 'Details'. |
threshold |
step size to increase ps after each iterarion. See also 'Details'. |
upper |
maximum value to search for solution of the integral equation to solve. See also 'Details'. |
original_phi |
original \{φ_i\} values. Only used for beta distribution. |
m1 |
first moment of the residuals. Used to compute |
m2 |
second moment of the residuals. Used to compute |
alpha_0 |
initial value for Newton-Raphson method for the parameter α. See also 'Details' and multiroot. |
beta_0 |
initial value for Newton-Raphson method for the parameter β. See also 'Details' and multiroot. |
k_0 |
initial value for Newton-Raphson method for the parameter κ. See also 'Details' and multiroot. |
lambda_0 |
initial value for Newton-Raphson method for the parameter λ. |
theta_0 |
initial value for Newton-Raphson method for the parameter θ. |
For the Zero-μ Laplace distribution the value of the corresponding integral equation has a closed solution of the form ps=-σ log2s.
For the other distributions, starting with the initial value of ps
passed as argument, the value, integral
, of the corresponding integral expression is
computed (see also 'References' for an in-depth explanation of this integral expression).
If integral
is smaller than 1-s
then ps
is increased
by a step size of threshold
value and integral
is recomputed.
If integral
is greater or equal than 0 or if ps
gets bigger than
upper
, the loop stops and the last value of ps
will be its final value.
In addition, for the Beta distribution values of parameters α and β are estimated using Newton-Raphson method.
For the Weibull distribution value of parameter κ is estimated using Newton-Raphson method and then estimated value of λ is computed using a closed form that depends on κ.
For the MOGE distribution values of parameters λ, α and θ are estimated using Newton-Raphson method.
See also 'References'.
Returns an object of class c("error_interval","list")
with information of the corresponding error interval.
Jesus Prada, jesus.prada@estudiante.uam.es
Link to the scientific paper
Prada, Jesus, and Jose Ramon Dorronsoro. "SVRs and Uncertainty Estimates in Wind Energy Prediction." Advances in Computational Intelligence. Springer International Publishing, 2015. 564-577,
with theoretical background for this package is provided below.
http://link.springer.com/chapter/10.1007/978-3-319-19222-2_47
error_interval
p_laplace
p_gaussian
p_beta
p_weibull
multiroot
p_moge
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 |
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