In the design of real-world complex engineering systems and infrastructure, one typically deals with scarce data. When only scarce data is available, convexity approaches are widely used to construct the uncertainty model in terms of bounds. Convex models estimate the uncertainty bounds using different bounding geometries that seek minimum volume with the available points. Chebyshev inequality in conjunction with geometries such as convex hull allows accounting for unobserved future data points by inflating the initially constructed geometry. Since the Chebyshev inequality is independent of the underlying distribution, the inflated convex geometry is often highly conservative. To address the conservativeness, we propose constructing a convex hull with a modified inflation coefficient that uses information on input dimension and spread of data. Since conventional metrics for the spread of data such as kurtosis is volatile when the sample is scarce, we use L-moments which are known to be robust to sample size. The initial convex hull built using samples from a distribution characterized by L-kurtosis is inflated incrementally until an allowable number of points corresponding to target probability is violated. The corresponding inflation coefficient is considered the modified coefficient. This exercise is repeated for different L-kurtosis and dimensions, and the modified inflation coefficient are obtained for different target probability as well to construct an empirical relationship between L-kurtosis, number of dimensions, and modified inflation coefficient.