lcd: Class 'lcd'
In cnmlcd: Maximum Likelihood Estimation of a Log-Concave Density Function

Class lcd is used to store a log-concave density function (f), where the log-density is given by a piecewise linear function.

Given an lcd object, the density function is defined by

f(x; alpha, theta, p, L, U) = C^(-1) exp{alpha (x - L) - sum_{j=1}^m p_j (x-theta_j)_+}, for x in [L, U],

where C is the normalizing constant given by

C = Integral_L^U e^{alpha (x - L) - sum_{j=1}^m p_j (x-theta_j)_+} dx.

coef, fk, dpk and cpk can all worked out from the given parameters. They are computed when a new lcd object is created by function new.lcd() to facilitate computation when the object is used later.

A list consisting of:

`alpha`	the slope of the log-density before the first interior knot.
`C`	the normalizing constant.
`theta`	vector of interior knots.
`pi`	vector of changes of slope at the interior knots.
`lower`	lower-boundary knot (L). This should be the smallest observed value.
`upper`	upper-boundary knot (U). This should be the largest observed value.
`coef`	a numeric matrix with two rows, with rows 1 and 2 storing, respectively, the intercepts and slopes of the log-density between knots.
`fk`	density values at the lower boundary (`lower`) and the interior knots (`theta`).
`dpk`	integral of x^o f(x) over each interval between knots for o = 0, 1, 2.
`cpk`	integral of x^o f(x) over each interval between the lower boundary and each knot.