In many cases, the log-frequency vs magnitude curves for earthquakes show considerable curvature, though the well-known G-R (Gutenberg-Richter) formula predicts a straight line. To represent such data, two modifications of the G-R formula have been proposed.
log n(M)=a-bM M≤c
n(M)=0 M>c} ()
and log n(M)=a-bM+log(c-M) M<c
n(M)=0 M≥c} (3)
These are called here the truncated G-R formula and the modified G-R formula, respectively. These equations can be written in the form of probability density function:
f(x)=/1--BCe^-Bx C≥x≥0 (5)
f(x)=/-+--Bx(C-x) C>x≥0 ()
where x=M-M_S, = ln 10, C=c-M_S, and M_S is the lower limit of magnitude above which the data is complete.
The estimation of and C in equation (5) by the method of moments was discussed by Okada (1970) and Cosentino et al. (1977). The equations proposed here are
expC(C-)/Cx-=--/- (16)
=(-C)/(-Cx) (15)
or /=-(+)/(e^BC-1)/1-/(e^BC-1) (18)
Bx=1-/(e^BC-1) (19)
The maximum likelihood method for equation (5) yields only one equation (equation (19), Page (1968), Okada (1970)). If we adopt C=Max(x_i) as the second equation, the C value is considerably biased. To correct the bias, a correction ΔC which is a function of and C is proposed. For this correction we must use some estimated values for and C.
To estimate and C in equation () by the method of moments the following equations are used.
/(-+-1){-(++)+-}/{-(+)+-}

2

(25)
Bx=

e

-

BC

(

BC

+

2

)+

BC

-

2

/

e

-

BC

+

BC

-1 (23)
The maximum likelihood estimates of

B

and C in equation (

6

) can be obtained by the equation:

2

-Bx=C/S ∑^S_i=1 1/C-x_i=

BC

(1-

e

-

BC

)/

e

-

BC

+

BC

-1 (27), (29)
The accuracy of

B

and C values determined by the above methods is estimated by Monte Carlo technique for the cases of S=50, 100, 200, 400, and 800 and several values of

B

and C. If we adopt the truncated G-R formula, the second method (which uses C=Max(x_i)+ΔC) gives more accurate C values, whereas the accuracy of

B

values is almost the same as that obtained by the method of moments. If we adopt the modified G-R formula, the maximum likelihood method gives more accurate

B

and C values than the method of moments. The η value (η=

x²

/

x²

) is a useful index for the deviation of the distribution of data from the G-R formula (for the G-R formula, theoretical value for η is

2

). An application of the present methods shows regional variations in

b

, c, and η values of shallow earthquakes in Japan.

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To improve the effect of chemotherapy of chronic myelogenous leukemic (CML) in blastic phase, the following clinical analysis were conducted.
1) The present study consisted of 53 adult patients with CML, who were registered to the nd Department of Medicine, Okayama University Hospital and diagnosed as blastic phase between from January 1970 to March 1980. There were 29 males and 24 females, and age ranged from 15 to 77 years (median: 41).
) These 53 patients were divided into 4 groups. i) Group I-A (5 cases) was diagnosed as blastic crisis () with hiatus leukemicus (HL) and initially treated with multicombination chemotherapy such as NCD, DMP or NCDP regimens (N: Neocarzinostatin, C: Cytosine arabinoside, D: Daunorubicin, M; -Mercaptopurine, P: Prednisolone). ii) Group I- (16 cases) was diagnosed as with HL and initially treated with VP or VPM regimens (V: Vincristine, P: Prednisolone, M: -Mercaptopurine). iii) Group II-A (11 cases) was early diagnosed as without HL according to our established criteria, and initially treated with multicombination chemotherapy such as NCMP, DCMP, NDMP, NCDP or NCDVP. and, iv) Group II- (21 cases) was early diagnosed as without HL and initially treated with VP, MP, or VPM.
3) Complete remission (CR) rate of each group was 20.0% in Group I-A, 56.% in Group I-, 27.3% in Group II-A and 47.% in Group II-.
4) Median survival and its surviving ranges after of each group were 3. months (1.8-4.5), .7 (1.0-24.), .0 (.-.8) and 13.0 (4.1-43.5). Median survival of CR-responders was 3., 10.0, 8.7 and 17.0 months, respectively.
5) The rate of one-year survivors of each group was 0%, 31.3% 9.1% and 52.4%.
) In conclusion, the most ideal approach to prolongation of the survival period of CML patients after entering is i) to diagnose as early and accurate as possible, and ii) to treat these patients initially with rather mild regimens such as VP or VPM, instead of aggressive regimens with multicombination drugs.

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