Using of information about Sƒ-equal-shoulder symmetry at the processing of censored data

F(t) possesses Sƒ -equal-shoulder symmetry property, if a distribution function satisfies to acondition( ) 1 ( ( ) F t = −F S t + 0),tR,where S(t) is continuous, decreasing and(S) 1(t) S(t), S( ) − = ƒ = ƒ ,(S) 1(t) − is inverse function for S(t), F(ƒ)= 0.5, ƒ is known center of symmetry.Note if S(t) = 2ƒ −t we receive the ordinary symmetry of distribution function concerningmedian value ƒF(t) =1−F(2ƒ −t +0).Theorem 1. If F(t) is continuous and increasing then F(t) satisfies to propertyF(t) =1−F(S(t)+ 0),tR,whereS(t)=F−1(1−F(t)),ƒ = F−1(0.5),F−1(t) is inverse function for F(t).Theorem consequence is that exponential, uniform and lognormal distributions are Sƒ -equalshouldersymmetrical.In this paper we use the knowledge about property (1) for estimating a distribution functionand its numerical characteristics on progressive censored sample( ) {( ) ( ) ( )} X,I = X1,I1,X2,I2,...,XN,IN ,where for i= 1,N0, full observation;1, censored observation;iiiXIX= ⎧⎨⎩ −−moment T1 and share g of censoring are non casual.The estimation is defined by2 ( )(1 )NS SN ti iiwhere { } ( ) 0: ,1: AIx x A x A = ∉  , for 1, i N =Smin{ , ( )},S1 ,Xi = XiS Xi Ii = −Ii S max{ , ( )},S 1 ,XN+i= Xi S Xi IN+i= −Ii (3)r is a number of full observations in [0,T1].

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