by @Armitage1969 to find the distribution of $Z_{(k)}$ conditional on reaching stage $k$.

In this manuscript, Section \[normality\] introduces notation for GSDs with stopping rules dependent on a parameter of interest and shows through a few examples of two-stage GSDs that conditional and unconditional distributions are truncated or mixtures of truncated distributions. Fisher information in MLEs is also derived in this section. Section \[mixtureD\] presents a method for designing a sequential experiment controlling a pre-determined power against a sequence of ordered alternatives while controlling type 1 error. This new approach does not use information fraction arguments and the design is fully driven by desired operational characteristics. Section \[LSP\] derives a local asymptotic distribution of the MLEs, which is a mixture of truncated normal distributions. Section \[example\] shows an illustrative application of the theory. Finally, Section \[Conclusion\] concludes this article with a short summary.

Likelihood in Group Sequential Designs {#normality}
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Consider a random variable $X$ with a p.d.f or a p.m.f. $f_X\left(x|\theta\right)$ and the objective of testing the null hypothesis $H_0:\theta=0$ with $\alpha$-level type 1 error and $1-\beta$ power at an alternative $H_1: \theta=\theta_1$. In GSDs, it is convenient to group the random sample in vectors corresponding interim analyses: $\mathbf{X}_{1}, 