<p>An important distribution for examining lifespan data and stress-strength reliability models is the Poisson Nadarajah–Haghighi (PNH) distribution because it is adaptable and useful for modeling survival data. Its failure rate can be increasing, decreasing, upside-down bathtub shaped, and bathtub-shaped. The means, variances, skewness, and kurtosis r-th order statistics are computed in this study by first deriving the exact explicit expressions for the single and double (product) moments of order statistics from the PNH distribution. Next, we obtain the maximum likelihood estimators of the unknown parameters and then constructed three parametric bootstrap confidence intervals, viz., standard bootstrap, percentile bootstrap and bias corrected percentile bootstrap of the parameters and compare them in terms of their average widths and coverage probabilities. Besides, we obtain best linear unbiased estimators (BLUE) for the location and scale parameters for the PNH distribution with known shape parameter are studied. Finally, two real data sets are used to illustrate the findings.</p>