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I would like to use and with my following sentence but I feel my structure is wrong.

We used lower and upper tails dependency shapes and positive and negative dependency shapes.

How can I use and with this sentence? any idea or help, please?

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    By far the neatest solution is to use as well as - although that doesn't answer your question. – Ronald Sole Dec 3 '18 at 13:52
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If you really wish to remain using and, then to improve the clarity of how the two items are grouped, I would suggest the use of ampersands in place of and in between lower and upper, e.g.:

We used lower & upper tails dependency shapes and positive & negative dependency shapes.

However, there are several ways in which you could avoid the and repetition entirely:

We used lower & upper tails dependency shapes in addition to positive & negative dependency shapes.

We used lower & upper tails dependency shapes as well as positive & negative dependency shapes. (credit: @RonaldSole)

We used lower & upper tails dependency shapes coupled with positive & negative dependency shapes.

(Though, that last option may depend somewhat on the context)

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Your structure doesn't seem to be incorrect, though there may be better ways to express its meaning.

You can also write it as:

We used shapes with both lower/upper tails dependency and positive/negative dependency.

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