pdfsmd

This function computes the probability density of the Singh--Maddala (Burr Type XII) distribution given parameters ($a$, $b$, and $q$) computed by <code>parsmd</code>. The probability density function is
$$f(x) = \frac{b \cdot q \cdot x^{b-1}}{a^b \biggl(1 + \bigl[(x-\xi)/a\bigr]^b \biggr)^{q+1}}\mbox{,}$$
where $f(x)$ is the probability density for quantile $x$ with $0 \le x \le \infty$, $\xi$ is a location parameter, $a$ is a scale parameter ($a &gt; 0$), $b$ is a shape parameter ($b &gt; 0$), and $q$ is another shape parameter ($q &gt; 0$).

distribution

probability density function

Distribution: Singh-Maddala

Distribution: Burr Type XII

Extensive functions for Lmoments (LMs) and probability-weighted moments (PWMs),
distribution parameter estimation, LMs for distributions, LM ratio diagrams, multivariate
Lcomoments, and asymmetric (asy) trimmed LMs (TLMs). Maximum likelihood and
maximum product spacings estimation are available. Right-tail and left-tail LM censoring
by threshold or indicator variable are available. LMs of residual (resid) and reversed
(rev) residual life are implemented along with 13 quantile operators for reliability analyses.
Exact analytical bootstrap estimates of order statistics, LMs, and LM var-covars are available.
Harri-Coble Tau34-squared Normality Test is available. Distributions with L, TL, and added
(+) support for right-tail censoring (RC) encompass: Asy Exponential (Exp) Power [L],
Asy Triangular [L], Cauchy [TL], Eta-Mu [L], Exp. [L], Gamma [L], Generalized (Gen) Exp
Poisson [L], Gen Extreme Value [L], Gen Lambda [L, TL], Gen Logistic [L], Gen Normal [L],
Gen Pareto [L+RC, TL], Govindarajulu [L], Gumbel [L], Kappa [L], Kappa-Mu [L],
Kumaraswamy [L], Laplace [L], Linear Mean Residual Quantile Function [L], Normal [L],
3p log-Normal [L], Pearson Type III [L], Polynomial Density-Quantile 3 and 4 [L],
Rayleigh [L], Rev-Gumbel [L+RC], Rice [L], Singh Maddala [L], Slash [TL], 3p Student t [L],
Truncated Exponential [L], Wakeby [L], and Weibull [L].

William Asquith

lmomco

L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments,
and Many Distributions

pdfsmd function

<dl> <dt>x</dt>
<dd>A real value vector.</dd> <dt>para</dt>
<dd>The parameters from <code>parsmd</code> or <code>vec2par</code>.</dd></dl>

Arguments

Author

Probability Density Function of the Singh--Maddala Distribution — pdfsmd

<dl>

 <dt>x</dt>
<dd>A real value vector.</dd>

 <dt>para</dt>
<dd>The parameters from <code>parsmd</code> or <code>vec2par</code>.</dd>

</dl>

pdfsmd: Probability Density Function of the Singh--Maddala Distribution

Description

Usage

Value

Arguments

Author

References

See Also