Monotonicity of HR(v)

Allocation Mechanism

Distribution (Proposition)

DHR

IHR

DIHR

IDHR

Market

Pure Lottery

Hybrid Lottery

Exponential Geometric (1)

X

X

Gamma (1)

X

X

X

X

Gompertz-Makeham (1)

X

X

Pareto (1)

X

X

Truncated Normal (1)

X

X

Uniform (1)

X

X

Weibull (1)

X

X

X

X

Gumbel (2)

X

X

X

Inverse Gaussian (2)

X

X

X

Log-normal (2)

X

X

X

Burr XII (1, 2)

X

X

X

X

Log-logistic (1, 2)

X

X

X

X

Beta (1, 3)

X

X

X

X

X

Exponential Power (1, 3)

X

X

X

X

X

Modified Weibull (1, 3)

X

X

X

X

X

Weibull Extension (1, 3)

X

X

X

X

X

Exponeniated Weibull (1, 2, 3)

X

X

X

X

X

X

X

Generalized Weibull (1, 2, 3)

X

X

X

X

X

X

X