A Simple Step-Stress Model for Lehmann Family of Distributions

Pal, Ayan; Samanta, Debasis; Mitra, Sharmishtha; Kundu, Debasis

doi:10.1007/978-3-030-62900-7_16

Cited by 7 publications

(4 citation statements)

References 18 publications

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“…For low to moderate sample sizes, interval estimates of the model parameters can be obtained using the parametric bootstrap CIs ‐percentile bootstrap CIs and bias adjusted percentile (BCa) bootstrap CIs. Parametric bootstrap CIs are well studied in the absence of cured fraction and similar ideas can be used in our case (see section 3.2 of Pal et al 11 for construction of percentile bootstrap CIs and section 4.2 of Pal et al 10 for bias adjusted percentile (BCa) bootstrap CIs).…”

Section: Point Estimation and Interval Estimationmentioning

confidence: 97%

“…If the sample size is not very big, the above asymptotic distribution (11) may not work well. Hence, the following parametric bootstrap (simulation) approach may be adopted to approximate the distribution of the test statistic LR = −2((l 0 − l 1 )).…”

Section: Non-asymptotic Approachmentioning

confidence: 99%

“…is the hazard function corresponding to the time-to-event distribution at the ith stress level. Based on this model, inferential treatment of SSALT data is considered recently by some authors, see for example Pal et al 10,11 and Samanta and Kundu. 12 Recently, Kannan and Kundu 2 discussed about a study on altitude decompression sickness (DCS) conducted by the Air Force Research Laboaratory (AFRL).…”

Section: Introductionmentioning

confidence: 99%

“…$$ is the hazard function corresponding to the time‐to‐event distribution at the

i

th stress level. Based on this model, inferential treatment of SSALT data is considered recently by some authors, see for example Pal et al 10,11 and Samanta and Kundu 12 …”

Section: Introductionmentioning

confidence: 99%

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Order restricted inference for a multiple step‐stress model with long‐term survivors for a general family of distributions

Pal

Mitra

Kundu

2023

Appl Stoch Models Bus & Ind

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In this article, we propose a failure rate based step‐stress accelerated life testing (SSALT) model assuming that the time‐to‐event distribution belongs to a fairly general family of distributions and the underlying population consists of long term survivors. With increase in stress levels, it is expected that the mean time to the event of interest gets shortened leading to an order restriction among the mean times‐to‐event. We propose here a method of obtaining order restricted maximum likelihood estimators (MLEs) based on expectation maximization (EM) algorithm coupled with the method of generalized isotonic regression technique. Additionally, we address the testing of hypothesis problem for the presence of long term survivors in the underlying population based on both asymptotic and non‐asymptotic approaches. To illustrate the effectiveness of the proposed method, extensive simulation experiments are carried out and a real data set is analyzed.

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Section: Point Estimation and Interval Estimationmentioning

confidence: 97%

Section: Non-asymptotic Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…$$ is the hazard function corresponding to the time‐to‐event distribution at the

i

th stress level. Based on this model, inferential treatment of SSALT data is considered recently by some authors, see for example Pal et al 10,11 and Samanta and Kundu 12 …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations