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### Show that $1-\Phi(x)$ is approximately $\varphi(x)/x$ for large $x$ (standard-normal random variable) [duplicate]

Demonstrate that, for a standard normal random variable: $$1-\Phi(x) \approx \frac{\varphi(x)}x$$ for large values of $x$.
3k views

### Calculating P-Value of a Z-Score without using Z-Table [duplicate]

I couldn't find any videos or documentation that shows how to calculate p-value of a z-score without using z-table. Isn't it possible or is it that hard? I know i can use scipy to get that ...
2k views

### How to calculate percentiles from z-scores [duplicate]

We often get reference tables to match z-scores with equivalent percentiles. Can anyone help me calculate percentiles from z-scores? What's the formula? Thank you.
1k views

### standard normal CDF in Excel (by hand) [duplicate]

i'm struggling hard to calculate the CDF in excel without using pre-built formulas. I have Z score and need to compute CDF of standard Normal distribution. Let's say i have column A with Z scores -...
368 views

### Calculating area under normal curve to the right of an extremely high z-score [duplicate]

This might be a little unusual, but please bear with me. I'm working on a theoretical exercise in chromatography (chemistry), a method that is used to separate different molecules. It is assumed that ...
80 views

### Asymptotic equivalence of the survival function of a standard Gaussian [duplicate]

My statistics teacher told us the following asymptotic result: $X \sim N(0,1)$ $$P(X > u) \underset{u \rightarrow +\infty}{\sim} \frac{1}{u} \exp\left(-\frac{u^2}{2}\right).$$ Do you know how to ...
70 views

### How to compute CDF probability of normal distribution [duplicate]

Possible Duplicate: Evaluate definite interval of normal distribution Title was changed and question edited bellow. How is possible that a probability density function defined as following can ...
55 views

### CDF for inverse normal distribution [duplicate]

Do you have any idea how I can get the cumulative distribution function (CDF) for inverse-normal (Gauusian) distribution? Modeler 18.2 doesn't have that specific function, and I need it to calculate a ...
42 views

### Formulae to Convert between z Critical Value and Confidence Level [duplicate]

What are the two formulae to convert between the two? For example, I have a z critical value of 3.00. With what formula can you convert this to ...
21 views

### How to calculate a p-value without using a lookup table [duplicate]

I'm looking for the formula to calculate a p-value for statistical hypothesis testing by hand without using the lookup table. I've found something here (Calculating P-Value of a Z-Score without using ...
20 views

### Help figuring out this Standard Normal Problem [duplicate]

Need to somehow prove P(Z less then z) is less then equation2 I dont know where to get started with this problem. Please help me figure out how to go about doing this problem. Thank you So do i need ...
2k views

### How to show that this integral of the normal distribution is finite?

Numerically, I have noticed that $$\int_{-\infty}^{\infty} \dfrac{\phi(x)^2}{\Phi(x)}dx < \infty$$ where $\phi$ and $\Phi$ are the standard normal pdf and cdf. However, I do not see how to prove it....
4k views

### How to compute the probability associated with absurdly large Z-scores?

Software packages for network motif detection can return enormously high Z-scores (the highest I've seen is 600,000+, but Z-scores of more than 100 are quite common). I plan to show that these Z-...
6k views

### Approximation of logarithm of standard normal CDF for x<0

Does anyone know of an approximation for the logarithm of the standard normal CDF for x<0? I need to implement an algorithm that very quickly calculates it. The straightforward way, of course, is ...