The following slides show the distribution of the absolute value and phase of the impulse and frequency response. The shape depends mostly on the value of $K$. A greater LoS component will result in a decrease in standard deviation, leading to a more concentrated and higher peak around the mean. Since only the first tap contains a LoS component in this model, it will be the only one affected by changes to $K$. All other taps always follow the distribution for $K=0$. Ideally, the first tap's probability density function (PDF) is given by [3] $$ p_{|a_0|}(\xi) = 2\dfrac{K+1}{P_{\tau_0}}\xi \cdot \exp\left[-\left(K + \dfrac{(K+1)\xi^2}{P_{\tau_0}}\right) \right] \cdot \mathrm{I_0}\left(2\xi\sqrt{\dfrac{K\left( K + 1 \right) }{P_{\tau,0}}}\right) $$ and PDF in the frequency domain is given by $$ p_{|H|}(\xi) = 2(\gamma_{H}K+1)\xi \cdot \exp\left[-\left(\gamma_{H}K + (\gamma_{H}K+1)\xi^2 \right) \right] \cdot \mathrm{I_0}\left(2\xi\sqrt{\gamma_{H}K\left(\gamma_{H}K + 1 \right)}\right). $$ The factor $\gamma_{H}$ is used to convert to a different definition of $K$ and is unimportant for understanding this demo. The function $\mathrm{I_0}(x)$ is the modified Bessel function of the first kind and zeroth order.

The phase is uniformly distributed over $[-\pi, \pi)$ and unaffected by any changes made to the parameters. For the sake of easier visual processing the the phase is normalized to $[-1, 1)$ resulting in a constant PDF with the value $1/2$.

[1] D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge: Cambridge University Press, 2005.
[3] N. C. Beaulieu, Chengshan Xiao and Yahong Rosa Zheng, “Novel Sum-of-Sinusoids Simulation Models for Rayleigh and Rician fading Channels,” IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, vol. 5, no. 12, pp. 3667–3679, 2006.
[5] S. O. Rice, “Statistical properties of a sine wave plus random noise”, The Bell System Technical Journal, vol. 27, no. 1, pp. 109–157, 1948.