Further modified forms of binomial and poisson distributions

Summary Some new type of modifications of binomial and Poisson distributions, are discussed. First, we consider Bernoulli trials of lengthn with success ratep up to time whenm times of successes occur, and then, changing the success rate to γp, we continue the remaining trial. The distribution of number of successes is called the modified binomial distribution. The Poisson limit (n tends to infinity andp tends to 0, keepingnp=λ) of the modified binomial is called the modified Poisson distribution. The probability functions of modified binomial and Poisson distributions are given (Section 1). A new concept of (m, γ)-modification is introduced and fundamental theorem which gives the relations between the factorial moments of any probability function and the factorial moments of its (m, γ)-modification, is presented. Then some lower order moments of the modified binomial and Poisson distributions are given explicitly (Section 2). The modified Poisson ofm=2 is fitted to the distribution of number of children for Japanese women in some age group. The fitting procedure is also presented (Section 3). Some historical sketch concerning the modification and generalization of binomial and Poisson distributions is given in Appendix. The Institute of Statistical Mathematics     

Elastic anomalies in 1T-TaS2

The temperature dependence of the resonant period in 1T-TaS₂ was measured using the resonant flexural vibration technique. From the close study on the effect of thermal cycles, it is suggested that the anomalous regions observed both on cooling down (183–193 K) and on warming up (218–282 K) were associated with the nearly commensurate-commensurate charge density waves (CDW's) phase transition.     

Muon capture in oxides using the lifetime method

The relative capture rate has been measured for muons stopping in 22 oxides. The experimental method was to detect the decay electrons and to use the unique lifetime signature to determine which element captures the muon.