Unless there is some rationale for reversing values, I find it rather arbitrary to do so and then hunt for a distribution that fits the data. Instead, I prefer to employ a distribution that can reasonably represent the data as they are collected.

Without knowing more specific information about the data presented here, it appears that values are collected on the range from 0 to 100. The beta distribution is defined on a closed interval and is flexible WRT skewness. That is, the beta distribution can be employed to represent distributions with positive skew, negative skew, or even no skew. If it is correct that values are collected on the range from 0 to 100, then the distribution does indeed have a closed interval. That alone might prompt one to look at the beta distribution. That the data are negatively skewed provides yet another reason to think the beta distribution might be appropriate. I would not that in addition to flexibility in modeling positive or negative skew, the beta distribution is also flexible with regard to kurtosis. Indeed, one can model data with a central modal value and negative kurtosis OR data that have have such positive kurtosis as to be a U-shaped distribution with modes at the extremes.

Estimating the beta distribution to the original (sample) data can be performed employing the code:

proc univariate data=sample;
var x;
histogram / endpoints=55 to 100 by 5
odstitle="Distribution of Sample Data"
beta(theta=0 sigma=100);
run;

Note that theta is the lower bound of the beta distribution and sigma is the LENGTH of the beta distribution (as opposed to the upper bound for the beta distribution). Note, too, that the histogram for X is generated from 55 to 100 by 5 instead of from 0 to 45 by 5. This is consistent with presentation of the histogram for Y from 0 to 45 since Y=100-X. The beta distribution seems to fit reasonably well.

It is interesting to note that since the beta distribution can model any sort of skew and due to its definition on a closed interval, the beta distribution can also be employed for the transformed data. If Y=100-X, and if X follows a beta distribution with theta=0 and sigma=100, then Y also has a beta distribution with theta=0 and sigma=100. Thus, we can examine how well the beta distribution performs at modeling the distribution of X compared to how well the lognormal, Weibull, and gamma do at modeling the transformed data by modeling Y with a beta distribution along with the other three distributions.

proc univariate data=Transform;
var Y;
histogram / endpoints=0 to 45 by 5
odstitle="Distribution of Reversed Data"
lognormal(threshold=0) Weibull(threshold=0) gamma(threshold=0)
beta(theta=0 sigma=100);
run;

Performance of the beta distribution is comparable to performance of the gamma distribution when examined against the transformed data. It seems to provide a reasonable fit to the transformed data. The lognormal distribution would appear to fit the transformed data better. But there is absolutely no a priori reason to think that a lognormal distribution would be appropriate AND the lognormal distribution does not have finite range which is suspected here. Thus, reason for choosing the lognormal distribution is based only on empirical best fit evidence rather than any theoretic arguments. In sample data (particularly if the sample size is small), it should not be surprising to find that the true theoretical distribution is not the best fitting distribution.

I specified parameters theta and sigma of the beta distribution. (Note that theta=0 is the default and didn't really need to be specified above). The beta distribution also has two additional shape parameters, alpha and beta. The relationship between alpha and beta determines both skewness and kurtosis. If beta>alpha, the distribution is skewed right. If alpha>beta, the distribution is skewed left. It may be observed from the estimates provided by the code above that these shape parameters are simply swapped when the transformed data is modeled instead of the sample data. That is, alpha(X)=beta(Y) and beta(X)=alpha(Y) where (X) and (Y) indicate modeling of variables X and Y, respectively.

There is much more that could be written on the beta distribution. But I think the above is sufficient for the problem given here. Hope this is of interest to some.