Normal vs. double exponential. For f0(x) = ex2/2/ 2, f1(x) = e|x| /2, the test of

Normal vs. double exponential. For f0(x) = e−x2/2/

√2π, f1(x) = e−|x|



/2, the test of the preceding problem reduces to rejecting when x2 i /

|xi| < C.

(Hogg, 1972.)

Note. The corresponding test when both location and scale are unknown is obtained in Uthoff (1973). Testing normality against Cauchy alternatives is discussed by Franck (1981).