**4.1** Arguing as in the examples,

which indicates that *Y* has the lognormal distribution with parameters *μ* + ln *c* and *σ*. Because no parameter was multiplied by *c*, there is no scale parameter. To introduce a scale parameter, define the lognormal distribution function as . Note that the new parameter *v* is simply *e*^{μ}. Then, arguing as before,

demonstrating that *v* is a scale parameter.

**4.2** The following is not the only possible set of answers to this question. Model 1 is a uniform distribution on the interval 0 to 100 with parameters 0 and 100. It is also a beta distribution with parameters *a* = 1, *b* = 1, and *θ* = 100. Model 2 is a Pareto distribution with parameters *α* = 3 and *θ* = 2000. Model 3 would not normally be considered a parametric distribution. However, we could define a parametric discrete distribution with arbitrary probabilities at 0, 1, 2, 3, and 4 being the parameters. Conventional usage would not accept this as a parametric distribution. Similarly, Model 4 is not a standard parametric distribution, but we could define one as having arbitrary probability *p* at zero and an exponential distribution elsewhere. Model 5 could be from ...

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