On the Generalized Lognormal Distribution

Table 1

Probability mass values 𝑃_𝛾;𝑖=Pr{𝑋_𝛾≤𝑖}, 𝑖=1/2,1,2,…,5, and the 1st and 3rd quartiles 𝑞_1;𝛾, 𝑞_3;𝛾 for various generalized lognormally distributed 𝑋_𝛾∼ℒ𝒩_𝛾(0,1).

𝛾	𝑃𝛾;1/2	𝑃𝛾;1	𝑃𝛾;2	𝑃𝛾;3	𝑃𝛾;4	𝑃𝛾;5	𝑞1;𝛾	𝑞3;𝛾
−50	0.2501	0.5000	0.7499	0.8326	0.8739	0.8987	0.4998	2.0008
−10	0.2505	0.5000	0.7495	0.8297	0.8698	0.8940	0.4990	2.0038
−5	0.2508	0.5000	0.7492	0.8264	0.8652	0.8887	0.4982	2.0071
−2	0.2515	0.5000	0.7485	0.8187	0.8539	0.8756	0.4964	2.0145
−1	0.2521	0.5000	0.7479	0.8097	0.8408	0.8601	0.4945	2.0223
−1/2	0.2524	0.5000	0.7476	0.7989	0.8248	0.8410	0.4925	2.0303
−1/10	0.2528	0.5000	0.7482	0.7757	0.7895	0.7984	0.4986	2.0426
1	0.1534	0.5000	0.8466	1.0000	1.0000	1.0000	0.6065	1.6487
3/2	0.2381	0.5000	0.7619	0.8848	0.9437	0.9721	0.5172	1.9334
2	0.2441	0.5000	0.7559	0.8640	0.9172	0.9462	0.5094	1.9630
3	0.2472	0.5000	0.7528	0.8505	0.8989	0.9267	0.5049	1.9804
4	0.2481	0.5000	0.7519	0.8452	0.8917	0.9188	0.5034	1.9867
5	0.2486	0.5000	0.7514	0.8425	0.8878	0.9145	0.5025	1.9899
10	0.2494	0.5000	0.7506	0.8375	0.8810	0.9068	0.5011	1.9954
50	0.2499	0.5000	0.7501	0.8341	0.8761	0.9013	0.5002	1.9992
±∞	0.2500	0.5000	0.7500	0.8333	0.8750	0.9000	0.5000	2.0000