Statistical properties of price sensitivity meter results

Price Sensitivity Meter (PSM) technique is used to estimate prices, which are maximal agreed to consumers. It is based on marketing survey of N target audience representatives' price preferences. The survey forms independent sample (X_H, Х_и, Х_и, X_M), k = 1, N, where for the k-th respondent X_k1 is minimal acceptable, X_k2 - bargain, X_k3 is high but yet acceptable, X_k4 is too high prices. For j = 1,4 the empirical distribution functions F (x) = zni 1[о*)()/n are considered, for i = 1,3 : S (x) = 1 - F (x) . The final prices are found as the abscissas of Fj (x), J = 2,4 and S, (x), i = 1,3 , intersections as x^(J) =|max|x:F_y(x) = S_t(x)|; x: S_t(x + 0)j(x)|, which are the medians' estimates x®) of G_tj(x) = (f(x) + Fj(x))/2. It was proved that x^(iJ) = X^j^ are (N + 1)-order statistics of a sample containing random values (X_ki,X.), k = 1, N, and x^(j are consistent and asymptotically normally distributed: L [4N (- xj N (0;v2), where v_v = ^2F (x(^J},x⁽jg.. (xj), F(у,z) is a joint of X,. and X_}, F (У,z) ф F(y)F (^z) because according to PSM for i,J = 1,4, i < j, prices X < X. and they are not independent; g.. (x) are the density function of G_tj(x) . Here we suggested that ^j for m = 1,4 3/_m (x) and g. (x(^J 5⁾) ф 0 . Equation (1) allows finding approximate confidence intervals x(N+1) - z(1_+r)/2 • v / VN < x®) < xN+1) + z_0+r)/2 • v / VN, where у e (0,1) is a confidence level, v..= 2F.I x^(j),x⁽ⁱ⁾ / | / ( x^(J} | + f. | x^(J} | | is consistent estimate of v.. based on the ,J V ,J I 0,5 0,5J/^, 0,5) ^j j | 0,5)) у sample containing (Х_й,X^), k = 1,N, z_(1+y)/2 is a ((1 + у)/2) - quantile of the standard normal distribution, g~ (x) is a consistent estimate of the density at x. The method was applied to calculate price of new software for B2B market. There were surveyed N = 52 target audience representatives. Some recommendations about pricing were given to the enterprise.

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