Confidence intervals for a two-parameter exponential distribution: One- and two-sample problems

Exact simultaneous location-scale tests for two shifted exponential samples

“…To illustrate the proposed two-sample tests, we analyse survival data from Krishnamoorthy and Xia [11]. This dataset consists of the number of survival days for patients with incurable lung cancer.…”

“…This dataset consists of the number of survival days for patients with incurable lung cancer. As in Krishnamoorthy and Xia [11], we consider two categories of patients' cancer type, i. e. squamous and small cells. There are m = 9 patients with squamous cell cancer type, and n = 9 patients with small cell cancer type, see Table 5.…”

“…For example, in the engineering sciences it is used to model the lifespan of electronic components, transmission, engine and mechanical equipment. Nevertheless, many researchers, including Huang, Mukherjee and Yang [8], Kao [10], Krishnamoorthy and Xia [11], Roy and Mathew [17], and Wu [27], have found that in various practical applications, such as measuring the reliability of a product, monitoring the high-voltage of current in certain metal oxide semiconductor transistor on a flash memory wafer, modelling the consumer lifetime, among others, the two-parameter (shifted) exponential distribution should be preferred to the one-parameter exponential distribution. The probability density function (pdf) of the two-parameter exponential distribution is f (x; θ, λ) = 1 λ exp −(x−θ)/λ ; x > θ > 0, λ > 0.…”

“…Sangnawakij and Niwitpong [18] proposed confidence intervals for the single coefficient of variation and the difference of coefficients of variation in the two-parameter exponential distributions. Krishnamoorthy and Xia [11] considered some problems related to estimating the confidence interval of the survival probability for a two-parameter exponential distribution. However, none of the existing works addressed combined testing of the two parameters in a comprehensive way.…”

Simultaneous monitoring of origin and scale of a shifted exponential process with unknown and estimated parameters

“…Research on the exponential and shifted exponential distributions for complete and censored data has been very active. One may see, among others, Wright et al, 1 Mitra and Patankar, 2 Baker et al, 3 Perry and Pignatiello, 4 Baklizi, 5 Doostparast and Balakrishnan, 6 Han et al, 7 Ganguly et al, 8 Cheng et al, 9 and Krishnamoorthy and Xia 10 . Kao 11 emphasized the importance of monitoring‐shifted exponential processes in the context of monitoring high voltage of current in a typical semiconductor transistor on a flash memory wafer.…”