FIR Filter Design - input parameters conversion
As I've mentioned in a comment, the Parks McClellan algorithm is usually used to design frequency selective filters with a fixed maximum stopband error, which results in an equiripple behaviour in the stopband. Note that the algorithm can in principle approximate any desired frequency response shape. However, many implementations just allow for piecewise constant desired responses (which includes all standard frequency selective filters, such as low pass, high pass, etc.).

If you want a frequency response that decays monotonically from the cut-off frequency, you probably want something like a Butterworth filter. This is an IIR filter which is usually designed via the bilinear transform from an analog prototype filter. If you want an FIR filter, then one option would be to truncate (or window) the infinite impulse response of the Butterworth filter.

In Matlab/Octave this can be easily done as follows. First design a digital Butterworth filter with the given specifications, compute its impulse response, and truncate it. Where to truncate depends on the error that you allow. For your example a third order Butterworth filter is sufficient. In the following example I assume a sampling frequency of $8\,\text{kHz}$:


[b,a] = butter(3,1.6/4);    % Butterworth IIR filter
h = impz(b,a,30);           % impulse response (30 coeffs)
f = logspace(0,3.6,400);    % log. frequency grid [1,4000]Hz
H = freqz(b,a,f*pi/4000);   % Butterworth frequency response
Hf = freqz(h,1,f*pi/4000);  % FIR frequency response
semilogx(f,20*log10(abs(H)),f,20*log10(abs(Hf)))
axis([1,4000,-80,5]), grid on




You see just a single curve because both filters (IIR and FIR) have virtually the same magnitude response.